Harmonic Source Modeling Techniques for Wide-Area Distribution System Monitoring: A Systematic Review

Abstract

With the increasing penetration of converter-based devices, harmonic distortion has become a major challenge for power quality monitoring in large-scale power systems. This study presents a systematic review of methods for modeling harmonic sources and their applicability to real-time monitoring of power distribution systems. The review was conducted following PRISMA guidelines, considering literature published between 2000 and 2026. Searches were performed across Scopus, IEEE Xplore, Web of Science, ScienceDirect, and MDPI using predefined keywords. A total of 128 peer-reviewed journal articles were included. Potential sources of bias were qualitatively assessed, including selection, retrieval, and classification bias; however, residual bias may still arise from database selection, keyword design, and study classification. A structured comparative framework is introduced, based on a six-dimension coverage scoring scheme and maturity analysis, enabling consistent evaluation across both methodological and deployment aspects. The robustness of this framework was evaluated using leave-one-out and perturbation analyses, indicating low variability in coverage scores and stable rankings across both corpora. A taxonomy of harmonic source modeling approaches is proposed. Comparative synthesis indicates that measurement-based approaches, particularly those leveraging distribution-level PMUs, show strong potential for real-time monitoring. Key challenges include D-PMU placement, data integration, and computational scalability. Future work should focus on physics-informed AI and digital twin-based monitoring.

1. Introduction

The rapid integration of new technologies in modern distribution systems, such as electric vehicle chargers, photovoltaic inverters, smart converters, and other power electronic-based devices, has significantly transformed the behavior of low- and medium-voltage networks. Modeling harmonic sources is essential for ensuring power quality, maintaining system reliability, and supporting the continued growth of advanced distribution technology integration.

1.1. Harmonic Challenges in Modern Distribution Systems

The shift towards carbon-free energy has led to a massive increase in converter-based nonlinear devices. These devices possess nonlinear voltage and current relationships and are commonly known as harmonic sources [1] which are the main sources of harmonic current injection, deteriorating power quality. These impacts can be characterized by considering long-established harmonic sources or equivalent models and detailing new and future sources and their probable effects to predict the amount and flow of harmonic currents generated by harmonic sources [1,2,3]. The operation of a power system is always uncertain owing to varying load conditions, variations in the power supply system, variations in the parameters of the components, and the operating conditions of the system. These conditions are discussed in detail in [4]. These parameters must be considered for accurate harmonic source models when developing the corresponding models.

1.2. Standards for Harmonics and Renewable Energy Integration

Harmonics tend to flow towards the utility because of the low impedance of the network compared with the loads. This results in harmonic propagation to other parts of the network. Analytical models for the representation of aggregate nonlinear loads in harmonic propagation and distortion studies were presented in [1,4,5,6,7], where single-phase and three-phase rectifiers were identified as the main sources of harmonic currents in industrial networks. Load models play a key role in the evaluation and testing of harmonic monitoring tools. Benchmark systems were presented in [8] for the development of new harmonic analysis methods and the evaluation of existing harmonic software. Several deterministic harmonic models have been reported in the literature. These models have been developed and categorized into residential, small commercial, industrial, and agricultural customers. The harmonic current emission of an industry consists of three factors based on the percentage of power used by the installed motors, the percentage of motors with Variable Speed Drives (VSDs), and the harmonic emission of the three-phase rectifiers [9].

The work presented in [10] revealed that, in active distribution systems, Current Total Harmonic Distortion (THDi) may no longer be suitable for harmonic evaluation, particularly in networks containing distributed generation. To correctly identify the loads at a given Point of Common Coupling (PCC), it is necessary to characterize the locally produced harmonics separately from those originating from the utility. One principle for assigning responsibility is that corrective action should fall to the originator of the problem [11]. Owing to the lack of field power quality measurements, it is often difficult to identify harmonic sources in distribution systems; in such cases, the utility must assume responsibility.

Background harmonics are often modeled as a voltage source in series with inductive and resistive components connected in parallel with loads and other harmonic sources at the point of common coupling [6]. Knowledge of these sources is crucial for designing harmonic filters at the PCC.

1.3. Importance of Harmonic Source Modeling

Harmonic source models are often based on active network measurements: current and voltage measurements are used to compute harmonic current magnitudes as percentages of the fundamental current, which are then used as inputs to the model in the chosen software tool [9]. Several approaches have been proposed. A measurement method that determines the source and harmonic impedance for residential and commercial systems supplied by a single-phase transformer and shows the utility and consumer contributions at the PCC via a short circuit controlled by a thyristor at the measuring point was presented in [12]. The main drawback of this method is the need to insert a thyristor into the measurement arrangement, which increases the cost compared to existing measurement systems. Methods capable of locating consumers responsible for harmonic disturbances in real time were presented in [13,14] using vector analysis, nonparametric density estimation, and Gaussian mixture models. Although these enable real-time analysis, each experiment analyzes only a single harmonic current. A fuzzy-logic algorithm that estimates the location and relative level of harmonic sources based on power magnitude, signal characteristics, and network reactance was proposed in [15].

Machine Learning Metamodel (MLM) methods for estimation and classification have been able to accurately predict the behavior of nonlinear loads; however, they require a database built from field measurements or electromagnetic-transient simulations to capture relationships between harmonic sources and the network under varying conditions [16]. The behavior of electronic converters was analyzed via time–frequency decomposition to observe time-varying harmonic phasors in [17]. That study showed that if a converter’s firing angle changes, the harmonic content becomes time-varying and can be used for identification. The transient behavior of AC/DC converters during instantaneous voltage sags reveals characteristic harmonic variations that are useful for load identification and protection analysis.

In [18], a load-disaggregation technique based on transient current signatures was presented; it used a simple, cost-effective three-stage artificial neural network with error backpropagation as the classifier and achieved reasonable performance. Network-wide real-time harmonic monitoring is required for utilities to assume responsibility for harmonic issues. Several methods have been proposed to monitor both the network and consumer contributions. In [19], a method based on a harmonic Norton equivalent circuit was presented to determine consumer and utility contributions at the PCC by separating the harmonic current and voltage into two components (one due to the consumer and one due to the grid). Other studies using Norton equivalents, for example, ref. [20], enable the evaluation of the relative contributions of multiple customers at the PCC; however, these techniques require an adequate and accurate equivalent circuit while multiple nonlinear loads are continuously changing.

The lack of sufficient real-time power quality measurements has hindered the development of wide-area monitoring tools owing to the inadequate synchronized online measurement equipment required to make the network fully observable [21], which also leads to epistemic uncertainty [4]. Synchrophasor measurements are expected to increase in future power networks. Distribution-level Phasor Measurement Units (D-PMUs) and Harmonic Phasor Measurement Units (H-PMUs) that can provide synchronized harmonic data with high time resolution are being rapidly developed and deployed [22,23].

1.4. Contributions and Literature Gap

This review presents a structured assessment of harmonic source modeling techniques from a unified viewpoint that considers their real-time deployment for wide-area distribution system monitoring.

1.4.1. Unified Evaluation Framework

Unlike previous reviews, which consider modeling techniques and deployment viewpoints in isolation, this review proposes a framework that enables a unified evaluation of harmonic source modeling techniques, real-time deployment perspectives, and wide-area distribution system monitoring requirements.

1.4.2. Systematic Comparison Across Modeling Approaches

This review classifies harmonic modeling techniques into four methodological categories: classical/analytical, measurement-based, data-driven (AI-based), and statistical/probabilistic. These approaches are evaluated within a unified framework that enables consistent comparison across methods previously examined in isolation, while explicitly distinguishing between methodological capability and validation realism. By incorporating real-time and wide-area considerations, the review links modeling choices to practical implementation. The analysis further identifies measurement infrastructure, data availability, and system-scale constraints as key factors limiting the deployment of existing methods.

1.4.3. Targeted Gap Analysis and Future Directions

The identified gaps in scalability, heterogeneous data integration, and weak coupling between physics-based and data-driven methods are mapped to targeted future research directions, including hybrid modeling methodologies, digital twin integration, and deployable learning frameworks. The remainder of the paper is organized as follows: Section 3.2 presents a detailed technical comparison of harmonic modeling techniques, structured according to the established taxonomy; Section 4 provides an explicit research gap analysis; Section 5 outlines future research directions; and Section 6 concludes the paper, as illustrated in Figure 1.

The following section outlines the systematic review protocol adopted to ensure a structured, transparent, and consistent analysis of the literature.

2. Review Protocol

This study presents a structured systematic literature review of harmonic source modeling techniques in power systems. The methodological approach is informed by established guidelines for evidence-based reviews in engineering, particularly those proposed by Kitchenham [24,25], and follows the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA 2020) framework to guide study identification, screening, and reporting [26].

The review protocol, including the search strategy, eligibility criteria, and selection procedure, was defined a priori. Two complementary sets of studies were constructed: one comprising review articles used to establish the scope and context of the field, and another comprising original research articles used for methodological classification and comparative analysis. Study selection and classification were performed using predefined criteria; however, elements of expert judgment remained inherent in these steps. The review was not prospectively registered in a systematic review registry.

The following subsections describe the literature search strategy (Section 2.1) and the structured eligibility criteria (Section 2.2), as well as the source selection procedures applied to (i) review articles for scoping purposes and (ii) original research articles for methodological classification and comparative analysis (Section 2.3). The review scope and methodological constraints are discussed in Section 2.4.

2.1. Search Strategy

To support both conceptual scoping and methodological comparison, two complementary study sets were constructed. The first set consists of review articles and is used to establish the taxonomy and overall research landscape of harmonic modeling techniques. The second set comprises primary research articles, which are used for detailed methodological analysis and comparison.

A systematic literature search was conducted across major scientific databases, including Scopus, IEEE Xplore, Web of Science, ScienceDirect, and MDPI (Energies). The search covered publications from 2000 to 2026 to capture both fundamental and recent developments and employed predefined keyword combinations, as shown in

Table A1. Preliminary database search strategy and parameters (2000–2026) for review scoping.

Database	Search Query/Keywords	Filters Applied	Notes
Scopus	(ALL(harmonics) AND ALL( “power systems”)) AND PUBYEAR > 1999 AND PUBYEAR < 2027 AND LIMIT-TO(DOCTYPE, “re”) AND (LIMIT-TO(SUBJAREA, “ENGI”) OR LIMIT-TO(SUBJAREA, “ENER”)) AND LIMIT-TO(LANGUAGE,“English”)	Review articles; English	Boolean search
IEEE Xplore	(“All Metadata”:harmonics) AND (“All Metadata”:review OR “systematic review”)	Journals only	Metadata + full-text
Web of Science	harmonics (All Fields) AND “power systems” (All Fields)	Article; Review Article	Topic search
ScienceDirect	harmonics AND “power systems”	Review articles	Full-text
MDPI Energies	harmonics	Engineering; Review; Journal: Energies	Journal filter

,

Table A2. Preliminary database search strategy and parameters (2000–2026) for methodological classification and analysis. * is a search wildcard meaning power system can be followed by any word.

Database	Search Query/Keywords	Filters Applied	Notes
Scopus	TITLE-ABS-KEY (((harmonic OR harmonics) W/3 (source OR sources OR injection OR emission OR responsibility)) OR “harmonic state estimation” OR ((harmonic OR harmonics) W/3 (measurement OR monitoring OR detection OR identification)) ) AND TITLE-ABS-KEY (“power system*” OR “distribution system* ” OR “distribution network*” OR “transmission system* ” OR grid) AND PUBYEAR > 1999 AND PUBYEAR < 2027 AND (LIMIT-TO (DOCTYPE, “ar”)) AND (LIMIT-TO (LANGUAGE, “English”)) AND (LIMIT-TO (SUBJAREA, “ENGI”) OR LIMIT-TO (SUBJAREA, “ENER”))	Article; English; Engineering/Energy	Boolean query with proximity operator
IEEE Xplore	((harmonic OR harmonics) NEAR/3 (source OR sources OR injection OR emission OR responsibility) OR “harmonic state estimation” OR (harmonic OR harmonics) NEAR/3 (measurement OR monitoring OR detection OR identification)) AND (“power system*” OR “distribution system*” OR “distribution network*” OR “transmission system*” OR grid)	Journals only	Metadata + full-text search
Web of Science	TS = (((harmonic OR harmonics) NEAR/3 (source OR sources OR injection OR emission OR responsibility) OR “harmonic state estimation” OR (harmonic OR harmonics) NEAR/3 (measurement OR monitoring OR detection OR identification)) AND (“power system*” OR “distribution system*” OR “distribution network*” OR “transmission system*” OR grid) )	Article; English	Topic search (title, abstract, keywords)
ScienceDirect	((“harmonic source” OR “harmonic injection” OR “harmonic emission”) OR (“harmonic state estimation” OR “harmonic monitoring”)) AND (“power system” OR “distribution system” OR “distribution network” OR “transmission system” OR grid)	Research articles	Full-text search
MDPI Energies	(harmonics) AND (“power systems” OR “distribution systems”) AND (“harmonic source” OR “harmonic state estimation” OR “harmonic monitoring” OR “harmonic detection” OR “harmonic identification”)	Engineering; Articles; Energies	Journal-specific filtering

and

Table A3. Construction and evaluation of screening text.

Stage	Operation	Details
Text extraction	Field selection	Title, abstract, and author-provided keywords are extracted from each BibTeX record. These fields are selected as they provide the highest information density for identifying methodological relevance.
Text aggregation	Unified representation	The extracted fields are concatenated into a single textual sequence to form a unified screening input, ensuring that matching rules are applied consistently across all available descriptive metadata.
Normalization	Text standardization	The aggregated text is converted to lowercase, punctuation is removed, and whitespace is normalized. Only alphanumeric characters and hyphens are retained to ensure robust and consistent keyword matching across heterogeneous BibTeX formats.
Exact phrase matching	Strong inclusion criterion	Predefined domain-specific phrases (e.g., “harmonic source model”, “harmonic source modeling”, “harmonic source modelling”, “harmonic source identification”, “harmonic source estimation”, “harmonic injection model”, “harmonic injection modeling”, “harmonic current source model”, “harmonic emission model”, “harmonic source characterization”, “harmonic source representation”, “wide-area harmonic monitoring”, “real-time harmonic monitoring”) are matched directly within the screening text. This rule captures studies with explicit and unambiguous relevance to harmonic source analysis.
Grouped keyword matching	Flexible inclusion criterion	A lead term ( (“harmonic”, [“source”, “sources”, “injection”, “emission”]), (“harmonics”, [“source”, “sources”, “injection”, “emission”]), (“model”, [“harmonic”, “harmonics”, “source”, “injection”]), (“modeling”, [“harmonic”, “harmonics”, “source”, “injection”]), (“modelling”, [“harmonic”, “harmonics”, “source”, “injection”]), (“estimation”, [“harmonic”, “harmonics”, “source”]), (“identification”, [“harmonic”, “harmonics”, “source”]), (“characterization”, [“harmonic”, “harmonics”, “source”, “emission”]), (“representation”, [“harmonic”, “harmonics”, “source”]), (“monitoring”, [“harmonic”, “harmonics”]), (“measurement”, [“harmonic”, “harmonics”]), (“real-time”, [“harmonic”, “harmonics”, “monitoring”]), (“wide-area”, [“harmonic”, “harmonics”, “monitoring”]), (“stochastic”, [“harmonic”, “harmonics”, “source”, “injection”]), (“probabilistic”, [“harmonic”, “harmonics”, “source”, “injection”]), (“statistical”, [“harmonic”, “harmonics”, “source”, “injection”]), (“measurement-based”, [“harmonic”, “harmonics”, “estimation”, “monitoring”]), (“data-driven”, [“harmonic”, “harmonics”, “estimation”, “monitoring”]), (“machine learning”, [“harmonic”, “harmonics”, “estimation”, “identification”]), (“artificial intelligence”, [“harmonic”, “harmonics”, “estimation”, “identification”]) must co-occur with at least one companion term within the screening text. This allows detection of relevant studies that use varied terminology while preserving contextual meaning.
Exclusion signal detection	Non-target identification	Terms associated with mitigation or filtering (e.g., “active power filter”, “passive power filter”, “hybrid power filter”, “harmonic filter design”, “filter tuning”, “harmonic mitigation”, “harmonic compensation”, “custom power device”, “thd reduction”, “thd improvement”, “power quality index”) are identified. These terms do not directly trigger exclusion but are used to detect potential scope conflicts when combined with inclusion signals.
Decision logic	Rule combination	Records are classified using a conservative logic: inclusion is assigned if either exact phrase or grouped keyword criteria are satisfied; records exhibiting both inclusion and exclusion signals are flagged for manual review; records without inclusion signals are excluded.

, which present queries and automated pre-screening rules, respectively. Methodological keywords were intentionally excluded to avoid bias toward specific approaches, and classification into methodological categories was performed during the analysis stage.

2.2. Eligibility Criteria

Eligibility criteria were defined separately for each corpus to reflect their distinct roles in the review.

(i)

Review study set: Peer-reviewed review or systematic review articles addressing harmonic modeling, detection, monitoring, or estimation in power systems, or provide a methodological discussion. This is used to support taxonomy development and contextual analysis.

(ii)

Research study set: Peer-reviewed research articles proposing, evaluating, or applying harmonic modeling and monitoring techniques, used for comparative methodological analysis.

(iii)

General criteria: Studies were required to be peer-reviewed journal articles, published in English and to provide sufficient methodological detail relevant to harmonic source modeling or monitoring.

Studies focusing solely on power quality indices without modeling content were excluded. The final set of included studies was analyzed in terms of methodological scope, technical depth, and relevance to deployment.

2.3. Study Selection Procedure

The study selection process was conducted separately for each corpus following a consistent screening workflow. Retrieved records were initially screened based on titles and abstracts using an automated pre-screening step. This was followed by an enhanced manual screening procedure implemented through a custom Python tool (version 3.12), which facilitates efficient review of BibTeX records (see Appendix B, Box A1). The tool parses each entry and presents the title, abstract, and keywords in an interactive interface, enabling rapid and traceable classification into included, excluded, or flagged categories.

Pre-screening was applied to journal article records exported in BibTeX format. Records were first merged and deduplicated using DOI matching where available, and normalized title–year matching otherwise. Titles, abstracts, and keywords were then evaluated using a rule-based combination of exact inclusion phrases and grouped keyword co-occurrence logic. Records satisfying both inclusion and exclusion conditions were conservatively flagged for manual review rather than automatically excluded. Final inclusion decisions were based on manual screening, followed by full-text assessment for eligibility. The automated pre-screening procedure is summarized in the flowchart shown in Appendix B, Figure A1.

While both corpora followed the same selection workflow, inclusion decisions were guided by corpus-specific criteria. Ambiguity was addressed by evaluating cross-methodological contributions independently and by adopting a conservative rule for intra-methodological cases, assigning the lower adjacent level when higher-level criteria were not fully satisfied to avoid overestimation. The overall process is summarized using a PRISMA-based selection framework, shown in Figure 2 and Figure 3. The final selection resulted in two complementary datasets: a set of 11 review articles [27,28,29,30,31,32,33,34,35,36,37] used for scoping and taxonomy development, and 128 research articles [1,3,4,6,7,9,15,22,23,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156] used for detailed methodological analysis and provided in the Supplementary Materials selected_studies Microsoft Excel file.

2.4. Review Scope and Methodological Constraints

This review focuses on peer-reviewed journal articles addressing harmonic source modeling, estimation, and monitoring in transmission and distribution systems. The scope includes publications from 2000 to 2026, capturing both foundational analytical models and the recent emergence of measurement-driven and data-driven approaches.

Several methodological constraints and potential sources of bias should be noted: (i) The search was restricted to major scientific databases and English-language journal articles, which may introduce selection bias by omitting relevant literature from technical reports, non-indexed venues, conference publications, and non-English sources; (ii) keyword-based retrieval may not capture all studies addressing harmonic modeling under alternative terminology, potentially affecting recall; (iii) the review emphasizes methodological classification and comparative analysis rather than quantitative performance synthesis, which limits the ability to assess comparative performance outcomes; (iv) the coverage scoring framework used to assess topic representation relies on qualitative interpretation of study content, which may introduce a degree of subjectivity despite the use of consistent evaluation criteria; and (v) study selection, eligibility assessment, and classification were conducted by a single reviewer using predefined criteria and a structured evaluation template, which ensures consistency but may introduce reviewer-related bias.

These sources of bias are inherent to the review design and are mitigated through the use of multiple databases, consistent evaluation criteria, and a structured screening workflow; however, they cannot be entirely eliminated.

Section 3 presents the analysis process of the selected study sets, covering methodological classification, coverage scoring, and comparative synthesis.

3. Harmonic Source Modeling: A Comparative Synthesis

This section presents a comparative analysis of harmonic source modeling approaches with explicit emphasis on their suitability for wide-area monitoring. Rather than describing individual methods in isolation, the discussion synthesizes the literature across four methodological paradigms (classical/analytical, measurement-based, data-driven/AI-based, and statistical/probabilistic) using a unified set of evaluation dimensions.

The analysis focuses on key system-level considerations, including observability, scalability, uncertainty handling, communication burden, and measurement requirements, together with deployment readiness in real-time and wide-area contexts. By mapping each methodological category onto these dimensions, the section highlights the conditions under which different approaches are effective, the assumptions that limit their applicability, and the trade-offs that emerge in practical deployment.

3.1. Synthesis of Review Evidence and Coverage Trends

The review corpus is first analyzed to assess the coverage of harmonic modeling approaches across key methodological dimensions described in

Table 1. Harmonic Modeling and Monitoring: Coverage Assessment of Selected Sources.

#	Aspect	Comprehensive (✓)	Partial (P)	Limited (L)	Not Covered (×)
1	Classical/Analytical	Explicit physics-based harmonic source models (harmonic load flow, Norton/Thévenin equivalents, impedance/admittance matrices, component-level models)	Analytical models present but not central to the contribution	Brief mention only	Absent
2	Measurement-Based	Harmonic sources identified or estimated directly from measurements (PMU/D-PMU, harmonic state estimation, observers, multi-point sensing)	Real measurements used but not for source identification or simulation measurements used for identification	Measurements only for validation	No measurements used
3	Data-Driven/AI	ML/DL is core to harmonic source modeling, localization, or prediction (RF, SVM, CNN, GNN, Transformers, etc.)	ML used only for preprocessing or feature extraction	AI/ML cited but not implemented	Not mentioned
4	Statistical/Probabilistic	Explicit stochastic harmonic source models or probabilistic harmonic load flow (e.g., Monte Carlo, random variables)	Statistics used only in evaluation	Distributions mentioned without explicit modeling	Deterministic only
5	Real-Time Deployment	Demonstrated online or near-real-time operation (streaming data, HIL, real-time simulators, runtime analysis)	Claimed feasible but not demonstrated	Mentioned as future work	Offline only
6	Wide-Area Focus	Multi-substation or system-wide harmonic propagation analysis	Large feeder or partial network studies	Single feeder with scalability claims	Component-level or local only
7	Validation Realism	Modeling supported by real-world deployment evidence (e.g., validation on real systems, field data, operational networks)	Modeling incorporates real-world elements (e.g., measured data) but lacks full system validation	Modeling validated only in simulation or synthetic environments	No modeling or no validation/application

Note 1: 1–4: Represent methodological categories. 5–6: Describe application scope (real-time considerations and wide-area applicability). 7: Reflects validation and deployment realism, indicating whether the approach is demonstrated in real systems, partially supported by real-world data, or validated only in simulation. Note 2: 7 is interpreted according to study type: for research articles, it reflects validation realism, whereas for review articles it captures the integration of modeling with deployment considerations. For review articles, this includes explicit linkage to real-time or wide-area applicability, measurement infrastructure, and operational use. A score of comprehensive (✓) indicates clear and coherent integration, Partial (P) incomplete coverage, Limited (L) brief mention, and Not covered (×) absence.

.

Table 2. Comparison of Review Articles on Harmonic Modeling.

Review	Year	1	2	3	4	5	6	7	Key Contribution	Limitations
[27]	2003	✓	×	×	×	L	P	×	Early system-level overview of harmonic analysis techniques using frequency- and time-domain methods.	Primarily offline analytical focus; limited consideration of measurement integration or deployment aspects.
[28]	2003	✓	×	×	×	×	P	×	Formalization of harmonic load-flow frameworks with deterministic solvers.	Model-based focus; no discussion of deployment or monitoring systems.
[29]	2007	P	L	×	×	✓	L	×	Review of real-time digital simulation (RTDS/HIL) for time-varying harmonics.	Focus on simulation rather than system-level monitoring or coordinated deployment.
[30]	2017	✓	✓	P	P	L	L	×	Overview of harmonic sources and mitigation in renewable-rich systems.	Limited treatment of deployment constraints and wide-area coordination.
[31]	2019	P	✓	L	×	L	L	×	Review of harmonic source detection at PCC using electrical indicators.	Primarily local analysis; lacks system-level deployment perspective.
[32]	2021	×	×	×	×	×	×	×	Overview of harmonic issues in renewable-dominated systems.	Does not address harmonic source modeling or deployment considerations.
[33]	2022	L	P	✓	P	L	L	×	Survey of AI-based methods for harmonic detection and estimation.	Limited discussion of real-world deployment and measurement infrastructure.
[34]	2023	✓	P	✓	P	×	P	P	Review of harmonic estimation techniques combining signal processing and learning.	Partial discussion of scalability; limited integration of deployment constraints.
[35]	2023	✓	P	×	P	×	L	×	Taxonomy of harmonic sources across different load types.	Component-level focus; limited system-level deployment considerations.
[36]	2024	P	P	P	×	L	L	P	Review of detection and estimation methods in dynamic environments.	Deployment discussed mainly at algorithm level; lacks system-wide integration.
[37]	2024	P	×	P	P	P	×	×	Review of harmonic mitigation in converter-based systems.	Device-level emphasis; limited system-wide monitoring perspective.
This Review	2025	✓	✓	✓	P	P	P	✓	Integrates modeling approaches with deployment constraints (real-time and wide-area) and provides a unified evaluation framework.	Focus on system-level synthesis; does not include experimental validation.

Legend: ✓ = Explicitly addressed; P = Partially addressed; L = Briefly mentioned; × = Not addressed. Aspects: (1) Classical/Analytical; (2) Measurement-Based; (3) Data-Driven/AI; (4) Statistical/Probabilistic; (5) Real-Time Considerations; (6) Wide-Area Monitoring; (7) Deployment Readiness.

compares the reviewed studies across methodological, application, and validation dimensions, summarizing their main contributions and reported limitations to highlight methodological strengths and research gaps.

A synthesis of key observations from the harmonic modeling literature is then presented. Figure 4 and Figure 5 visualize research trends based on review articles published between 2000 and 2026. Figure 4 illustrates the temporal coverage intensity of key harmonic aspects, where darker shades indicate more comprehensive coverage, while Figure 5 shows the average emphasis placed on each aspect per publication year.The coverage scores are computed according to the formulation defined in Appendix C.

Figure 4 shows a transition from dominance of classical and measurement-based methods toward increasing contributions from data-driven approaches, while deployment-related aspects particularly deployment readiness remain comparatively underdeveloped until recent years. Figure 5 highlights a clear methodological transition from early dominance of classical/analytical approaches toward increasing integration of measurement-based and data-driven methods, particularly after 2017. While methodological diversity improves over time, the convergence observed in recent years reflects complementarity rather than the replacement of approaches. However, this evolution is not matched by deployment maturity: real-time capability and wide-area focus improve only gradually, and deployment readiness remains lagging until very recent years. This gap suggests that advances in modeling have outpaced practical implementation, with scalability, infrastructure dependence, and validation constraints limiting translation into operational systems.

Figure 6, shows the maturity index scores of the four harmonic source modeling techniques classical/analytical (2.25), measurement-based (1.5), data-driven/AI (1.42), and statistical/probabilistic (1.00) together with their practical extensions toward real-time deployment (1.00), wide-area monitoring (0.92), and deployment readiness (0.58) as shown in Equation (A4). The results indicate strong consolidation of physics-based and measurement-driven approaches, while data-driven and probabilistic methods remain less mature, reflecting ongoing challenges in robustness, validation, and scalable deployment. These trends remain stable under limited robustness checks, with only minor variations observed among closely ranked aspects and no change in the overall conclusions.

3.2. Comparative Analysis of Harmonic Modeling Techniques

In power systems, harmonic-source modeling is crucial for predicting and analyzing the behavior of harmonic sources. This section systematically compares harmonic source modeling techniques, organized into distinct methodological categories. The assessment guideline for the classification of selected articles is presented in Table 1 is also used.

Table 3. Harmonic Modeling Approaches: Methodological Characteristics.

Category	Representative Methods	Key Characteristics	Data Requirements	Computational Complexity
Classical/Analytical	Norton/Thévenin equivalents; harmonic load flow; impedance and admittance models; time-domain equivalents	Physics-based, deterministic, highly interpretable, sensitive to parameter accuracy	Complete network parameters	Medium–High ($O\left(n^3\right)$)
Measurement-Based	Direct measurements; harmonic state estimation; phasor-based methods; compressive sensing; D-PMU; WLS	Measurement-driven, synchronized, reduced dependence on network models	Real-time, Synchronized phasor measurements streams	Low–Medium
Data-Driven/AI	ANNs; CNNs; physics-aware neural networks; SVMs; random forests; deep learning ensembles	Nonlinear mapping capability, data-intensive, limited physical interpretability	Labeled historical datasets	High (training)/Low (inference)
Statistical/Probabilistic	Probabilistic harmonic power flow; Monte Carlo simulation; point estimate methods; Bayesian inference	Explicit uncertainty modeling, confidence bounds, planning-oriented	Statistical source models	Very High (Monte Carlo)/Medium (analytic)

and

Table 4. Harmonic Modeling Approaches: Deployment and Performance Comparison.

Category	Scalability to Wide-Area	Real-Time Capability	Robustness to Uncertainty	Typical Use Cases	Refs.
Classical/Analytical	Low	Low	Low	Offline studies, harmonic planning, benchmarking	[27,35,36,40,57,64,97,110,125,132,158,159]
Measurement-Based	High	High	High	Wide-area harmonic monitoring, event and disturbance analysis	[22,40,70,92,95,106,112,116,140,160]
Data-Driven/AI	High	High	Medium–High	Fast harmonic detection, classification, and pattern recognition	[15,115,118,119,121,161,162]
Statistical/Probabilistic	Medium	Low	High	Risk assessment and uncertainty-aware harmonic planning	[53,77,79,126,163]

present a structured comparison of the considered methodological categories, followed by detailed discussions of representative methods, their strengths and limitations, and their relevance to wide-area monitoring.

Table 4 complements Table 3 by extending the comparison from methodological characteristics to practical deployment considerations and observed performance.

Specifically, Table 3 outlines how each class of methods is formulated and what it requires in terms of data and computation, whereas Table 4 evaluates how these characteristics translate into scalability, real-time capability, and robustness in wide-area settings. Together, the tables highlight not only distinctions between categories but also their points of convergence, particularly in emerging hybrid approaches such as physics-informed AI, measurement-assisted analytical models, and probabilistic extensions of data-driven methods.

Taken together, Table 3 and Table 4 reveal a set of structural trade-offs across methodological categories. Analytical methods rely on detailed physical models, reducing measurement requirements but limiting scalability and introducing sensitivity to parameter uncertainty. Measurement-based approaches improve practical observability and enable real-time operation, but depend on extensive instrumentation and communication infrastructure. Data-driven methods enhance scalability and inference speed, yet remain dependent on data quality and generalization capability. Probabilistic approaches explicitly represent uncertainty, but incur significant computational cost and are less suited to real-time deployment.

These trade-offs indicate that no single methodological category simultaneously satisfies observability, scalability, uncertainty handling, and real-time deployment requirements for wide-area harmonic monitoring, motivating hybrid frameworks that combine complementary strengths. Temporal trends were also examined to show the transition from classical formulations to AI-enabled and wide-area frameworks.

3.2.1. Classical/Analytical Harmonic Modeling Methods

Table 5. Classical/Analytical Harmonic Modeling Methods: Summary of Formulations and Characteristics.

Method/Refs.	Representative Model	Mathematical Formulation	Key Assumptions	Strengths	Limitations
Norton/Thévenin Equivalent [40,57,90,159]	Harmonic source represented as equivalent current/voltage with impedance	${\displaystyle I=YV}$	Linear network, known impedance parameters	Simple, interpretable, widely used	Sensitive to parameter accuracy; limited scalability
Harmonic Load Flow (HLF) [40,115,140]	Frequency-domain nodal analysis using admittance matrix	${\displaystyle Y\left(h\right)V\left(h\right)=I\left(h\right)}$	Accurate frequency-dependent admittance and load models	System-wide harmonic propagation analysis	High computational cost ($O\left(n^3\right)$); parameter sensitivity
Time-Domain Models [90]	State-space or differential equation-based load models	${\displaystyle \dot{x}=f(x,u)}$	Detailed component-level modeling	Captures transient and nonlinear dynamics	High computational burden; complex modeling
Arc Furnace Model and other harmonic loads [6,61]	Nonlinear time-varying harmonic source (Fourier-based)	${\displaystyle u\left(t\right)=\sum _k{U}_{k}sin(k\omega t+{\phi }_k)}$	Balanced operation; dominant odd harmonics	Captures nonlinear and stochastic behavior	Complex harmonic coupling; difficult parameterization
Diode Bridge Rectifier [164]	Pulse-based harmonic current injection model	${\displaystyle I_k=\frac{8\alpha I}{\pi }\frac{cos\left(k\alpha \pi \right)}{1-k^2{\alpha }^2{\pi }^2}}$	No background harmonics; periodic operation	Analytical harmonic spectrum estimation	Simplified operation; ignores system interaction
Multi-Pulse Power Link (MPPL) [165]	Switching-function-based AC/DC harmonic interaction	${\displaystyle v_{dc}\left(t\right)=V_a{S}_a+V_b{S}_b+V_c{S}_c}$	Ideal switching functions; known DC current behavior	Links AC/DC harmonic interactions	Requires accurate switching and DC modeling
Inverter-Based Models [7,151]	Harmonic current source representation (characteristic harmonics)	${\displaystyle {\underline{U}}_{\mathrm{background}}={\underline{U}}_{\mathrm{U}-h}={\underline{U}}_{\mathrm{PCC}-h}-{\underline{I}}_{\mathrm{PCC}-h}·{\underline{Z}}_{\mathrm{U}-h}.}$	Assumes inverter model, known	Grid forming inverter harmonic characterization, accounts for background harmonics	Single-point; DG/EV impacts not explicit
Interharmonic Models (Converters) [154]	Frequency interaction between rectifier and inverter stages	${\displaystyle f_i=f_h\pm f_r}$	Known pulse number and modulation characteristics	Captures interharmonic generation	Sensitive to control strategy and operating conditions
Distributed Generation (DG) Models [45,60,65,67]	Converter-based DG modeled as harmonic sources	${\displaystyle Z_T\left(h\right),Z_N\left(h\right)}$ Transformer impedance, network impedance, current source	Converter-dominated generation; steady-state analysis	Suitable for renewable integration studies	Requires detailed converter modeling

summarizes the key formulations and assumptions underlying classical harmonic modeling approaches, highlighting their strengths and limitations in relation to scalability and deployment. These methods provide strong physical interpretability and form the foundation for harmonic propagation analysis. However, their applicability to wide-area monitoring is constrained by model-driven observability requirements, reliance on accurate network parameters, limited scalability for system-wide applications, and challenges in real-time deployment. These limitations motivate the integration of measurement-based and hybrid approaches in practical wide-area monitoring systems.

Analytical approaches remain fundamental for harmonic modeling due to their strong physical interpretability and well-established mathematical formulations. However, their performance in wide-area monitoring contexts depends critically on the availability and accuracy of network parameters, which directly affects system observability. In practice, parameter uncertainty, network reconfiguration, and the increasing penetration of converter-based resources limit the reliability of purely model-based approaches. Furthermore, while methods such as harmonic load flow provide system-wide analysis, their computational requirements and need for detailed modeling hinder real-time scalability. As a result, analytical methods are most effective as baseline or validation tools, rather than standalone solutions, in wide-area monitoring frameworks.

3.2.2. Measurement-Based Approaches

Measurement-based approaches, summarized in

Table 6. Measurement-Based Harmonic Modeling Methods: Summary of Characteristics and Formulations.

Method/Refs.	Representative Model	Mathematical Formulation	Key Assumptions	Strengths	Limitations
Harmonic State Estimation (HSE) [51,95,96]	Estimation of harmonic voltages and source currents from redundant measurements	${\displaystyle \widehat{x}={\left(H^{T}WH\right)}^{-1}{H}^{T}Wz}$	Quasi-steady-state; sufficient measurement redundancy	Robust to noise; statistical confidence; handles incomplete data	Requires redundancy; sensitive to measurement placement
D-PMU-Based Hierarchical Methods [22,23,118]	Wide-area synchronized harmonic phasor measurement and source contribution analysis	${\displaystyle V_h\left(t\right),I_h\left(t\right)}$ from synchronized phasors	Accurate synchronization; sufficient D-PMU deployment	High temporal resolution; wide-area observability; source attribution	Requires infrastructure; communication and data management challenges
Compressive Sensing Approaches [127,160]	Sparse harmonic source reconstruction from limited measurements	${\displaystyle {min\parallel x\parallel }_1\mathrm{s}.\mathrm{t}.Ax=b}$	Harmonic source sparsity	Reduced measurement requirements; efficient for incomplete monitoring	Sensitive to sparsity assumption; placement-dependent
PMU-Based Harmonic Estimation [23,106,118,166,167]	Extended synchrophasor measurement including harmonic and inter-harmonic data	${\displaystyle V_h^{\left(k\right)},I_h^{\left(k\right)}}$ phasor representation	Accurate synchronization; extended PMU protocol	Real-time monitoring; standardized data structure	Limited harmonic resolution; data handling complexity
Wide-Area Measurement Framework [40,62,112,139,167]	Combined fundamental, harmonic, and inter-harmonic data streams	${\displaystyle \{V_a,V_{ah}^{\left(k\right)},V_{ih}^{\left(k\right)}\}}$	Reliable communication and synchronized sampling	Comprehensive spectral visibility; suitable for WAMS	Increased data volume; processing complexity
Harmonic Spectrum-Based Modeling [168,169]	Harmonic injection derived from measured current spectrum	${\displaystyle |I_h|=I_{\mathrm{fund}}\left|\frac{I_h}{I_1}\right|}$; ${\displaystyle {\theta }_h={\theta }_h+h({\theta }_{\mathrm{fund}}-{\theta }_1)}$	Availability of historical harmonic spectra	Realistic modeling; captures load-specific behavior	Depends on data quality; limited adaptability to changing conditions
Harmonic Aggregation Models [170,171]	Aggregation of multiple harmonic sources considering phase interactions	${\displaystyle I_{\mathrm{agg}}=\sum _h{I}_h{e}^{j{\theta }_h}}$	Phase relationships between voltage and current	Simplifies system-level analysis	Sensitive to phase variation; may over/underestimate THD
Micro-Synchrophasor (µPMU) Monitoring [172,173]	High-resolution distribution-level synchronized measurements	${\displaystyle V\left(t\right),I\left(t\right)}$ with high temporal resolution	Dense sensor deployment; communication reliability	Fine-grained visibility; suitable for distribution networks	Cost; data synchronization and communication challenges

, rely on synchronized system measurements and estimation techniques rather than explicit circuit-based models. This enables direct observability of harmonic behavior, reducing dependence on detailed network parameterization and improving adaptability under changing operating conditions.

Measurement-based approaches address several of the key limitations associated with analytical methods by enabling direct system observability through synchronized measurements. In particular, D-PMU and HPMU technologies provide time-synchronized harmonic phasor data, reducing reliance on detailed network parameterization and improving robustness under changing operating conditions. These methods support near-real-time or real-time monitoring, making them well-suited for wide-area applications. However, their effectiveness depends on measurement infrastructure deployment, including device density, placement, and communication reliability. In addition, challenges remain in terms of data quality, synchronization errors, and the integration of heterogeneous measurement sources. Consequently, while measurement-based approaches significantly enhance observability and real-time capability, they introduce new dependencies related to infrastructure and data management.

3.2.3. Data-Driven/AI-Based Methods

Data-driven and AI-based approaches, summarized in

Table 7. Data-Driven/AI-Based Harmonic Modeling Methods: Summary of Characteristics and Formulations.

Method/Refs.	Representative Model	Mathematical Formulation	Key Assumptions	Strengths	Limitations
Artificial Neural Networks (ANNs) [116,119]	Multilayer perceptron mapping voltage inputs to harmonic currents	${\displaystyle {\widehat{I}}_h=f_{\theta }(V_1,\dots ,V_h)}$	Availability of labeled training data; stationarity of patterns	Captures nonlinear relationships; fast inference	Data-intensive; limited interpretability (black-box)
Physics-Aware Neural Networks [121]	Neural networks with embedded physical constraints	${\displaystyle \mathcal{L}={\mathcal{L}}_{data}+\lambda {\mathcal{L}}_{physics}}$	Partial knowledge of system physics; hybrid modeling validity	Improved generalization; reduced data requirements; interpretable	Requires domain expertise; still data-dependent
Multi-Source Data Fusion [115]	Integration of power quality, operational, and external data sources	${\displaystyle \widehat{y}=f(V,I,Z,W,D)}$${\displaystyle \mathrm{W}\text{-}\mathrm{weather}}$, ${\displaystyle \mathrm{D}\text{-}\mathrm{dispatch})}$	Availability of heterogeneous data streams	Captures external influences; improves prediction accuracy	High integration complexity; data synchronization challenges
Support Vector Machines (SVM) [33,84]	Regression-based harmonic source estimation	${\displaystyle \widehat{y}=\sum _i{\alpha }_{i}K(x_i,x)}$	Kernel selection and representative training data	Good generalization; effective with limited data	Sensitive to kernel choice; limited scalability
Machine Learning Metamodels (MLM) [161]	Surrogate models approximating harmonic relationships	${\displaystyle \left(\begin{array}{c}{\overline{I}}_1\\ ⋮\\ {\overline{I}}_h\end{array}\right)=f\left(\left(\begin{array}{c}{\overline{V}}_1\\ ⋮\\ {\overline{V}}_h\end{array}\right),R,L,P\right)}$	High-quality simulation or measurement data	Reduces computational cost; flexible modeling	Sensitive to training data quality; limited extrapolation
Fuzzy Systems [33]	Rule-based inference for harmonic classification/estimation	${\displaystyle y=\sum _i{w}_i\left(x\right)y_i}$	Expert-defined rules; linguistic variable representation	Interpretable; handles uncertainty	Rule design complexity; limited scalability
Decision Trees/Ensemble Methods [33]	Tree-based regression or classification models	${\displaystyle \widehat{y}=\sum _m{T}_m\left(x\right)}$	Representative training dataset	Interpretable (trees); robust to noise (ensembles)	Overfitting risk; limited extrapolation capability
Resonance Detection (ML-Based) [85,113]	Noninvasive detection using learned signal patterns	${\displaystyle \widehat{y}=f\left(x_{signal}\right)}$	Availability of labeled disturbance patterns	Effective for event detection; real-time capable	Limited physical interpretability; data dependency

, extend measurement-based methods by leveraging machine learning techniques to extract patterns from harmonic data. Rather than relying solely on explicit physical models, these approaches enable scalable analysis of complex, high-dimensional datasets and support multi-source data fusion in wide-area monitoring systems. In particular, AI-based methods are well-suited to complement measurement-based approaches by improving estimation accuracy, enabling predictive capabilities, and facilitating the integration of heterogeneous data sources.

AI-based approaches address scalability and complexity challenges that arise in measurement-based frameworks, particularly in large-scale and data-rich environments. Techniques such as neural networks, support vector machines, and physics-informed models enable efficient processing of high-dimensional data and support real-time or near real-time inference. However, these methods introduce new challenges related to model interpretability, generalization under changing system conditions, and dependence on the quality and representativeness of training data. Furthermore, their deployment in practical systems requires careful consideration of computational constraints, model updating, and integration with existing monitoring infrastructures.

3.2.4. Statistical/Probabilistic Methods

The statistical and probabilistic methods, summarized in

Table 8. Statistical/Probabilistic Harmonic Modeling Methods: Summary of Characteristics and Formulations.

Method/Refs.	Representative Model	Mathematical Formulation	Key Assumptions	Strengths	Limitations
Probabilistic Harmonic Power Flow (PHPF) [77,79,133,174]	Stochastic mapping between voltage harmonics and harmonic injections	${\displaystyle I_h=g_h(U_1,U_2,\dots ,U_h)}$	Uncertainty modeled through probabilistic input variables (voltage harmonics, sources)	Captures nonlinear harmonic interactions; supports probabilistic analysis	Computationally demanding; depends on accurate statistical characterization
Monte Carlo Simulation [4,129,133,174]	Repeated sampling of input distributions with deterministic harmonic analysis	${\displaystyle \mathbb{E}\left[y\right]\approx \frac{1}{N}\sum _{i=1}^N{y}^{\left(i\right)}}$	Large number of independent samples; known input distributions	Flexible; provides full output distributions	Very high computational burden; not suitable for real-time
Point Estimate Methods [77,175]	Approximation of output statistics using selected deterministic samples	${\displaystyle y\approx \sum _i{w}_{i}f\left(x_i\right)}$	Input distributions approximated by finite representative points	Reduced computation compared to Monte Carlo	Accuracy depends on distribution assumptions; limited generality
Kernel Density Estimation (KDE) [14]	Nonparametric estimation of harmonic current distributions	${\displaystyle {\widehat{f}}_b\left(x\right)=\frac{1}{nb}\sum _{i=1}^{n}K\left(\frac{x-x_i}{b}\right)}$	Availability of sufficient measurement samples	Flexible distribution modeling; no parametric assumption	Sensitive to bandwidth selection; data-dependent
Stochastic Harmonic Aggregation [1,124,129]	Probabilistic summation of harmonic vectors	${\displaystyle I_h^{\left(\mathrm{AGG}\right)}={\mathrm{DF}}_h\sum _{i=1}^m\left(a_i\right)\left(I_h^{\left(i\right)}\right)}$	Independence or known correlation of harmonic sources and diversity factor	Captures variability of aggregated loads	Sensitive to phase assumptions; complex modeling
Time-Series/DFT-Based Models [176]	Temporal evolution of harmonic components using signal decomposition	${\displaystyle X\left(k\right)=\sum _{n=0}^{N-1}x\left(n\right)e^{-j2\pi kn/N}}$	Stationarity over observation window	Captures time-varying harmonics	Limited predictive capability; data-dependent
Gaussian Mixture/Nonparametric Models [14]	Statistical modeling of harmonic injections using mixture distributions	${\displaystyle p\left(x\right)=\sum _{i=1}^{C_N}{\varphi }_i\mathcal{N}\left(x\right|{\mu }_i,{\sigma }_i)}$	Harmonic behavior follows multimodal distributions	Captures complex stochastic behavior	Model selection complexity; requires large datasets
Uncertainty Modeling (Load/Source Variability) [53,129]	Representation of load and source parameters as random variables	${\displaystyle R=R_{dc}(1.0+A{h}^B)}$	Known statistical characteristics of loads and sources	Enables realistic system modeling	Requires accurate statistical characterization

, extend deterministic modeling approaches by explicitly accounting for uncertainty in harmonic sources, system parameters, and operating conditions. Unlike analytical and measurement-based methods, which typically provide point estimates, these approaches characterize harmonic behavior in terms of probability distributions and stochastic processes. These methods are particularly relevant in modern distribution systems with high penetration of converter-based resources, where variability and uncertainty play a significant role in harmonic emission and propagation.

Probabilistic approaches provide a systematic framework for capturing uncertainty in harmonic modeling, enabling risk-aware analysis and more robust system assessment. Techniques such as Monte Carlo simulation, stochastic load modeling, and probabilistic harmonic load flow allow the evaluation of variability in harmonic distortion levels under different operating scenarios. However, these methods typically incur high computational cost and are often unsuitable for real-time deployment. Their accuracy depends on the availability of representative statistical models and sufficient data for parameter estimation. As such, probabilistic methods are most effective when integrated with measurement-based and data-driven approaches, where they can enhance uncertainty quantification and support decision-making in wide-area monitoring systems.

Taken together, the reviewed methodologies form a complementary framework for harmonic modeling and monitoring in modern distribution systems illustrated in Figure 7. Classical/analytical approaches provide the physical foundation for understanding harmonic propagation, while measurement-based methods enable real-time observability and system-wide visibility. Data-driven and AI-based techniques extend these capabilities by supporting scalable analysis and predictive modeling in data-rich environments. Statistical and probabilistic methods further augment the framework by explicitly capturing uncertainty and enabling risk-informed assessment. Rather than operating in isolation, these approaches are most effective when integrated, with measurement infrastructure serving as the backbone, analytical models providing physical consistency, AI enhancing scalability and inference, and probabilistic methods supporting uncertainty-aware decision making.

3.3. Temporal Evolution and Maturity–Growth Analysis

The temporal evolution of harmonic source modeling approaches is analyzed using era-level maturity and topic-level maturity–growth representations. Figure 8 and Figure 9, the former captures overall progression in coverage, while the latter highlights long-term development across methodological categories. See Equations (A4) and (A6), respectively.

In Figure 8a the methodological categories show a clear shift toward data-driven approaches, which increase from limited representation in early eras to substantial coverage in recent periods, while classical and measurement-based methods remain consistently high. In Figure 8b, the validation realism and application-oriented aspects exhibit limited progression over time. Validation realism remains within the partial validation range, while real-time capability fluctuates and wide-area applicability remains consistently low. These results indicate that methodological advances are not matched by corresponding improvements in validation depth or operational scalability.

Although data-driven methods dominate recent growth in Figure 9; they remain associated with lower levels of validation realism, suggesting that their adoption has outpaced the development of rigorous validation practices. This decoupling suggests that the rapid methodological advancement of data-driven approaches has not yet been matched by equivalent progress in validation realism, highlighting a gap between model development and empirical validation.

3.4. Robustness of Coverage Scoring and Maturity Analysis

The robustness of the coverage scoring framework was assessed using leave-one-out (LOO) resampling and discrete score perturbation ($\pm 1$ within $[0,3]$). For each test, topic-level maturity indices were recomputed and compared to the baseline results.

The results show that the maturity scores remain very stable across all methodological and deployment dimensions. The largest changes are small—0.273 (about 9.1% of the scoring range) under leave-one-out and 0.167 (about 5.6%) under perturbation. Ranking shifts occur in 10.1% of perturbation cases, but only among categories with very similar baseline scores, and there are no reversals between clearly different maturity levels. Overall, this suggests that the framework produces consistent conclusions, with any variation reflecting minor numerical differences rather than the influence of individual scoring decisions.

3.5. Harmonic Standards Compliance

Harmonic standards such as IEEE 519 (2022) [177], EN 50160 [178], and IEC 61000-3-6 [45,179] define compliance requirements in terms of voltage distortion limits, current emission constraints, and statistical performance metrics evaluated over specified time windows. These requirements impose distinct analytical, measurement, and operational needs across planning, monitoring, and control stages.

Table 9 summarizes the role of different modeling approaches across the system lifecycle. However, to establish a direct link between modeling techniques and regulatory compliance tasks, Table 10 maps the reviewed methods to specific standard requirements, measurement needs, and operational time scales.

In planning studies, compliance with IEEE 519 and IEC 61000-3-6 is typically verified using analytical harmonic load flow models, supplemented by probabilistic methods to account for variability in loads and network conditions. These approaches evaluate worst-case and statistical scenarios to ensure that harmonic limits at the PCC are satisfied under anticipated operating conditions.

Operational compliance assessment, particularly under EN 50160, relies on measurement-based approaches using power quality monitors and D-PMUs to evaluate harmonic distortion over defined aggregation intervals (e.g., 95th percentile metrics). These methods reflect the stochastic and time-varying nature of harmonic emissions in distribution systems.

Real-time compliance monitoring and responsibility allocation at the PCC primarily depend on synchronized measurement-based techniques, such as harmonic state estimation and hierarchical monitoring, which enable source identification and attribution. AI-based methods complement these approaches by providing fast inference, anomaly detection, and short-term prediction of potential violations.

Predictive compliance and control, supported by IEEE 1547.1 [180] and emerging grid-support requirements, increasingly rely on data-driven and hybrid methods that integrate measurement data with learning-based models to anticipate violations and support corrective actions.

At the equipment level, compliance with IEC 61000-3-2 and IEC 61000-4-7 [100] is ensured through analytical modeling and signal processing techniques, including FFT-based harmonic analysis under controlled testing conditions. Measurement-based methods form the foundation for real-time compliance and responsibility allocation, analytical and probabilistic methods remain essential for planning and risk assessment, and AI-based approaches enhance scalability and predictive capability. This structured mapping clarifies the complementary roles of each methodology in achieving end-to-end harmonic compliance in modern distribution systems.

Table 9. Harmonic Standards Compliance of Reviewed Methodologies Across System Life-cycle.

Standard(s)	Phase	Primary Model	Supporting Models	Purpose
IEEE 519 [119,177,179,181,182], IEC 61000-3-6 [35,45,135]	Design & Planning	Classical/Worst-case	Statistical/Probabilistic	Verify harmonic limits at PCC under worst credible operating conditions
EN 50160, IEC 61000-3-6 [79,135,136]	Operational Assessment	Measurement-Based	Statistical (95th percentile)	Demonstrate compliance over representative time windows; acknowledge short-term, random, intermittent nature of residential loads
IEEE 1547.1, DSTU EN 50160 [77,111,121]	Operational Forecasting	Data-Driven/AI	Measurement-Based	Anticipate limit violations and support corrective control actions
DSTU EN 50160 [178], IEEE 1547.1 [23,121,180]	Real-Time Monitoring	Measurement-Based	AI/Edge Computing	Detect dynamic violations and issue predictive alerts synchronized measurements
IEC 61000-3-2, IEC 61000-4-7 [39,100]	Equipment Certification	Equipment Harmonic Models	Signal Processing (FFT)	Ensure device-level emission compliance and instrument conformity
All (Life-Cycle) [103,125,183]	Post-Event & Adaptation	Hybrid (Physics + Data)	Statistical/Learning-Based	Refine models, update thresholds, and maintain continuous assurance

Table 9. Harmonic Standards Compliance of Reviewed Methodologies Across System Life-cycle.

Standard(s)	Phase	Primary Model	Supporting Models	Purpose
IEEE 519 [119,177,179,181,182], IEC 61000-3-6 [35,45,135]	Design & Planning	Classical/Worst-case	Statistical/Probabilistic	Verify harmonic limits at PCC under worst credible operating conditions
EN 50160, IEC 61000-3-6 [79,135,136]	Operational Assessment	Measurement-Based	Statistical (95th percentile)	Demonstrate compliance over representative time windows; acknowledge short-term, random, intermittent nature of residential loads
IEEE 1547.1, DSTU EN 50160 [77,111,121]	Operational Forecasting	Data-Driven/AI	Measurement-Based	Anticipate limit violations and support corrective control actions
DSTU EN 50160 [178], IEEE 1547.1 [23,121,180]	Real-Time Monitoring	Measurement-Based	AI/Edge Computing	Detect dynamic violations and issue predictive alerts synchronized measurements
IEC 61000-3-2, IEC 61000-4-7 [39,100]	Equipment Certification	Equipment Harmonic Models	Signal Processing (FFT)	Ensure device-level emission compliance and instrument conformity
All (Life-Cycle) [103,125,183]	Post-Event & Adaptation	Hybrid (Physics + Data)	Statistical/Learning-Based	Refine models, update thresholds, and maintain continuous assurance

Table 10. Mapping of Harmonic Modeling Approaches to Compliance Tasks and Standards.

Compliance Task	Relevant Standard(s)	Suitable Methods	Measurement Requirement	Time Scale/Application
Planning compliance verification (THD, harmonic limits at PCC)	IEEE 519, IEC 61000-3-6	Classical/Analytical + Probabilistic	Network parameters + statistical load models	Offline studies, scenario analysis
Operational compliance assessment (95th percentile limits)	EN 50160	Measurement-Based + Statistical	Continuous voltage/current measurements (PQ monitors, D-PMU)	Minutes to weeks (aggregation windows)
Real-time compliance monitoring and violation detection	IEEE 519 (monitoring), EN 50160	Measurement-Based + AI/Edge	High-resolution synchronized measurements (D-PMU)	Sub-second to seconds
Responsibility allocation at PCC/source identification	IEEE 519 (current limits, PCC responsibility)	Measurement-Based (HSE, hierarchical) + AI	Multi-point synchronized measurements	Near real-time/event-based
Predictive compliance/preventive control	IEEE 1547.1, EN 50160	Data-Driven/AI + Measurement-Based	Historical + streaming measurements	Seconds to minutes (forecast horizon)
Equipment-level emission compliance	IEC 61000-3-2, IEC 61000-4-7	Analytical + Signal Processing	Laboratory measurements, FFT-based analysis	Testing/certification phase

Table 10. Mapping of Harmonic Modeling Approaches to Compliance Tasks and Standards.

Compliance Task	Relevant Standard(s)	Suitable Methods	Measurement Requirement	Time Scale/Application
Planning compliance verification (THD, harmonic limits at PCC)	IEEE 519, IEC 61000-3-6	Classical/Analytical + Probabilistic	Network parameters + statistical load models	Offline studies, scenario analysis
Operational compliance assessment (95th percentile limits)	EN 50160	Measurement-Based + Statistical	Continuous voltage/current measurements (PQ monitors, D-PMU)	Minutes to weeks (aggregation windows)
Real-time compliance monitoring and violation detection	IEEE 519 (monitoring), EN 50160	Measurement-Based + AI/Edge	High-resolution synchronized measurements (D-PMU)	Sub-second to seconds
Responsibility allocation at PCC/source identification	IEEE 519 (current limits, PCC responsibility)	Measurement-Based (HSE, hierarchical) + AI	Multi-point synchronized measurements	Near real-time/event-based
Predictive compliance/preventive control	IEEE 1547.1, EN 50160	Data-Driven/AI + Measurement-Based	Historical + streaming measurements	Seconds to minutes (forecast horizon)
Equipment-level emission compliance	IEC 61000-3-2, IEC 61000-4-7	Analytical + Signal Processing	Laboratory measurements, FFT-based analysis	Testing/certification phase

3.6. Real-Time Deployment Considerations

Real-time deployment approaches focus on integrating harmonic monitoring algorithms into operational systems with strict latency and reliability requirements. Representative techniques include: (1) embedded D-PMU algorithms, which perform harmonic phasor estimation and source identification directly within D-PMU firmware [22,40,167]. This reduces communication overhead and enables low-latency processing through distributed computation, but is constrained by limited onboard resources and firmware update complexity. (2) Hierarchical monitoring architectures, which organize monitoring into local (substation), regional, and system-wide layers with structured data aggregation [22,184]. This improves scalability, reduces communication burden, and supports localized control actions; however, it introduces coordination challenges and potential inconsistencies between local and global estimates. (3) Edge computing implementations, where AI-based inference models are deployed at network edge devices to enable real-time processing [112,184]. This approach reduces reliance on centralized infrastructure, lowers latency, and enhances privacy, but is limited by computational constraints and model deployment complexity. These approaches align closely with operational requirements and support real-time, wide-area monitoring and control. However, they require significant infrastructure investment, as well as continuous maintenance and calibration. In practice, effective deployment relies on a hierarchical architecture that integrates measurement, communication, and edge intelligence.

4. Research Gaps and Limitations

Despite significant progress in harmonic source modeling, as highlighted in Section 3.2, several critical gaps continue to limit the deployment of comprehensive wide-area monitoring systems, as shown in Figure 9. This section systematically identifies these gaps, organized by technical dimensions.

Table 11. Research Gaps in Wide-Area Harmonic Monitoring and Source Identification.

Gap Category	Specific Gap	Impact on Wide-Area Monitoring	Current Maturity Level	Priority
Integration Challenges	Incomplete D-PMU coverage	Limits system-wide harmonic source identification and observability	Low	High
	Heterogeneous data fusion	Reduces estimation accuracy and reliability due to inconsistent data formats and resolutions	Medium	High
	Communication constraints	Prevents real-time centralized or coordinated harmonic analysis	Medium	Medium
Scalability	Computational complexity	Limits feasible network size for real-time harmonic estimation	Medium	High
	Hierarchical frameworks	Results in incomplete multi-scale monitoring and coordination across system levels	Low	High
	Field validation at scale	Introduces uncertainty regarding real-world performance and robustness	Low	Medium
Real-Time Processing	Latency versus accuracy tradeoff	Delays mitigation actions and operational decision-making	Medium	High
	Embedded resource constraints	Limits deployment of advanced analytics and edge AI solutions	Medium	Medium
Data Quality	Limited training data for AI models	Reduces generalization capability and robustness of data-driven methods	Low	High
	Incomplete feeder-level monitoring	Increases estimation uncertainty and obscures localized harmonic sources	Medium	Medium
	Measurement errors	Degrades overall estimation accuracy and confidence in results	Medium	Medium
Source Identification	Attribution under aggregation	Complicates harmonic responsibility assignment among multiple sources	Low	High
	Time-varying and stochastic sources	Limits attribution accuracy for modern loads and DERs	Low	High
	Lack of standardized metrics	Hinders regulatory enforcement and consistent responsibility allocation	Low	Medium

Maturity Levels: Low = early research stage; Medium = demonstrated in limited contexts; High = mature with field deployments. Priority: Based on the impact on wide-area monitoring deployment and urgency for utility applications.

summarizes the identified research gaps and their impacts on wide-area monitoring, current maturity levels, and associated priorities.

4.1. Summary of Research Gaps

Table 11 summarizes the identified research gaps and their impacts on wide-area monitoring deployment.

4.2. Integration Challenges with Modern Monitoring Infrastructure

In this study, we identified three main research gaps.

4.2.1. Incomplete D-PMU/H-PMU Coverage and Optimal Placement

D-PMUs/H-PMUs are gradually being deployed in distribution networks, and some studies specifically address harmonics [23,185]. The use of D-PMUs for harmonic analysis is still emerging. In practice, D-PMU deployments remain sparse and uneven, which makes system-wide identification of harmonic sources difficult [22,186,187]. When placement is considered, existing optimization methods are typically designed to ensure observability for state estimation, not to improve harmonic source identification [188,189,190]. Consequently, even well-placed units may offer limited insight into the origin of harmonics. This problem is further compounded by the fact that many D-PMUs capture only aggregated behavior at the subarea level, forcing reliance on hierarchical attribution techniques that remain imperfect [22]. There is a clear need for placement strategies tailored specifically to harmonic monitoring algorithms that prioritize source identification while respecting budget constraints, as well as estimation methods that remain reliable despite incomplete and aggregated measurements.

4.2.2. Heterogeneous Data Streams and Reporting Rates

Modern distribution system monitoring draws on a mix of data sources that differ widely in sampling rate, timing accuracy, and overall reliability [187]. D-PMUs provide tightly synchronized phasor measurements at high rates, typically between 10 and 120 samples per second [191]. At the other end of the spectrum, AMI smart meters report aggregated information at much slower intervals, often every 15 min to an hour. Supervisory Control and Data Acquisition (SCADA) systems sit in between, offering substation-level measurements updated every few seconds, while power quality monitors generate detailed, high-resolution waveforms only when specific events are detected. These disparities highlight the need for multi-rate data fusion frameworks that can intelligently combine heterogeneous measurements, cope with synchronization errors and missing data, and rigorously track how uncertainty propagates across different data streams.

4.2.3. Communication Architecture and Bandwidth Constraints

Wide-area monitoring generates substantial volumes of data that can rapidly exceed the capacity of contemporary communication infrastructure [22]. High-rate D-PMU streams, particularly those that incorporate detailed harmonic phasors, may surpass the bandwidth limitations of legacy networks. Concurrently, the utilization of public Internet links or cellular backhauls introduces unpredictable delays, complicating the support of applications that rely on timely data. Centralized systems encounter difficulties in managing this data volume, as channeling all measurements to a control center creates bottlenecks and increases costs, thereby highlighting the necessity for more distributed processing architectures [192,193]. It is imperative to explore edge and fog-based architectures that can distribute harmonic processing closer to the data sources, reduce the volume of raw data requiring transmission, and enhance algorithmic tolerance to latency.

4.3. Scalability to Wide-Area Systems

4.3.1. Computational Complexity of Network-Wide Estimation

The computational complexity associated with network-wide estimation presents significant challenges, particularly in the context of large distribution systems. Classical harmonic load flow and comprehensive network state estimation exhibit poor scalability [184]. In particular, the inversion of the nodal admittance matrix, with a complexity of $O\left(n^3\right)$, is impractical for networks comprising thousands of nodes. Furthermore, real-time constraints pose difficulties, even for medium-sized networks consisting of 500–1000 nodes, in terms of real-time processing capabilities. Consequently, research efforts should focus on the development of reduced-order models and hierarchical decomposition methods. Additionally, the exploration of graph neural networks that leverage the sparsity of network topology and the implementation of parallel processing algorithms are imperative.

4.3.2. Hierarchical and Partitioned Monitoring Strategies

Although previous studies have explored hierarchical methods for harmonic monitoring in power systems [155,194,195], a comprehensive framework facilitating coordinated monitoring across multiple grid levels remains largely undeveloped. The increasing penetration of nonlinear loads, power electronic converters, and distributed energy resources has intensified harmonic interactions, creating a need for monitoring strategies that maintain consistent harmonic source attribution across feeders, substations, and system-wide perspectives. Existing studies primarily focus on harmonic detection, estimation, and aggregation techniques; however, they often lack mechanisms to ensure consistency across hierarchical levels or network partitions [36,114]. Moreover, harmonics frequently propagate beyond predefined partition boundaries, complicating the analysis of cross-region interactions and coordinated mitigation efforts [52,196,197]. Determining appropriate aggregation levels for different applications, ranging from local diagnostics to system-level planning, remains an open research challenge. These limitations highlight the need for formalized multiscale harmonic monitoring frameworks with provable consistent aggregation and disaggregation methods, validated using real utility network data.

4.3.3. Limited Field Validation at Large Scale

Most studies on harmonic monitoring and analysis have primarily assessed the proposed methods using small-scale benchmark systems, such as the IEEE 13-bus and IEEE 37-bus networks, through simulation studies [39,198,199,200],also observed in Figure 9. Although these evaluations are useful for initial validation, they offer a limited understanding of how these methods would perform in actual distribution networks, which consist of thousands of nodes, a variety of load types, and substantial levels of distributed energy resource (DER) penetration. Consequently, questions concerning scalability remain largely unaddressed. Moreover, numerous practical challenges associated with real-world implementation, such as sensor calibration errors, communication disruptions, data quality issues, and ongoing maintenance requirements, are seldom addressed in current research studies. To address these gaps, it is essential to foster closer collaboration with electric utilities to enable large-scale field trials, develop open datasets from real distribution networks, and create benchmark test systems that more accurately represent the complexity of contemporary power grids.

4.4. Real-Time Processing Limitations

4.4.1. Latency Requirements vs. Algorithm Complexity

Real-time harmonic mitigation requires the rapid identification of distortion sources, often within seconds, whereas many accurate estimation techniques rely on several minutes of measurement data to achieve reliable results [40,95]. This mismatch creates a fundamental trade-off between response latency and estimation accuracy. For example, prior studies have reported harmonic state estimation based on 15-min data windows, with improved performance at a 3-min resolution; however, this temporal resolution remains insufficient for fast-acting mitigation strategies [95]. In addition, many iterative estimation algorithms require multiple measurement cycles to converge, further delaying the availability of actionable results. Another unresolved challenge is the ability to distinguish short-lived transient harmonic events from persistent sources, which is critical for avoiding unnecessary or ineffective mitigation actions. These limitations highlight the need for fast approximate algorithms with bounded accuracy guarantees and event-triggered estimation approaches that adapt the temporal resolution in response to changing system conditions. Predictive models that anticipate harmonic behavior before it fully develops may also help bridge the gap between real-time requirements and algorithmic complexity.

4.4.2. Computational Resource Constraints in Embedded Systems

The implementation of AI-based analytics on edge devices, such as H-PMUs and intelligent electronic devices, is becoming increasingly appealing. However, this approach is accompanied by significant resource constraints. These devices generally possess restricted memory and processing capabilities, which pose challenges in deploying deep neural networks without exceeding hardware constraints. Even lightweight models may encounter difficulties in meeting real-time inference deadlines when operating on resource-limited embedded platforms. Furthermore, once models are deployed in the field, updating them to accommodate evolving system conditions or enhanced algorithms can be operationally complex and costly. Addressing these challenges necessitates the development of power-system-specific model compression techniques and the design of hardware-aware neural network architectures. Additionally, robust online update mechanisms are crucial to ensure that deployed models can be maintained and improved throughout their operational lifespan [201,202,203].

4.5. Data Quality and Availability Issues

4.5.1. Limited and Noisy Training Datasets for AI Methods

Data-driven and AI-based methods depend on large, high-quality labeled datasets; however, such datasets are scarce in power system applications [119,121]. In practice, ground-truth harmonic source currents are rarely measured directly, requiring labels to be inferred or generated through simulations, which introduces additional uncertainty. Historical datasets are often highly imbalanced, with rare but critical harmonic events, such as resonance conditions, appearing infrequently. Moreover, domain shift remains a significant challenge, as models trained on one network frequently fail to generalize to systems with different topologies, load compositions, or operating conditions. Addressing these limitations requires the development of transfer learning and domain adaptation techniques that enable cross-network generalization, as well as semi-supervised and self-supervised learning approaches that reduce the reliance on labeled data. In addition, synthetic data generation frameworks based on validated power system models can help expand and diversify training datasets.

4.5.2. Incomplete Feeder-Level Monitoring

The direct monitoring of every distribution feeder is economically impractical, leaving large portions of the network unobserved [115]. Consequently, feeder-level harmonic behavior must often be inferred from indirect measurements, such as substation-level data, which inherently introduces uncertainty into the estimation process. Validation is particularly challenging in these cases because ground-truth measurements are typically unavailable at unmonitored locations. Future research should focus on probabilistic estimation methods that explicitly quantify the uncertainty at unobserved feeders. Active learning frameworks that guide strategic sensor placement can further reduce uncertainty while minimizing additional instrumentation, and advanced metering infrastructure data may offer valuable Supplementary Information for indirect validation.

4.5.3. Measurement Errors and Calibration Drift

Measurement accuracy is further affected by errors introduced by instrument transformers and sensing devices [187]. Current and voltage transformers exhibit frequency-dependent magnitude and phase errors that can significantly distort harmonic measurements, particularly at higher frequencies. Over time, sensor calibration drift can degrade measurement accuracy unless periodic recalibration is performed. Synchronization errors represent an additional concern because disruptions in GPS-based timing systems can introduce phase inconsistencies across measurement points. Addressing these issues requires robust estimation algorithms that explicitly account for realistic measurement error models. Online calibration techniques that exploit redundant measurements can help correct drift in real time, whereas calibration-free approaches based on relative or differential measurements provide promising alternatives when absolute calibration cannot be guaranteed.

4.6. Harmonic Source Identification and Responsibility Assignment

4.6.1. Attribution Under Aggregated Measurements

Accurately attributing responsibility to individual contributors when system measurements capture the aggregated impact of multiple harmonic sources is inherently challenging [6,22]. Harmonic sources operating at similar frequencies can produce superposition effects that are difficult to decompose using conventional measurement and analysis techniques. In addition, sources exhibiting correlated temporal behavior, such as multiple Photovoltaic (PV) inverters responding to a common irradiance profile, further obscure individual contributions and complicate source attribution. Therefore, blind source separation techniques must be developed. These approaches should exploit temporal diversity and frequency-domain signatures to enhance source discrimination and further explore causality-based analysis methods to support reliable attribution.

4.6.2. Time-Varying and Stochastic Source Behavior

Modern loads and distributed energy resources (DERs) exhibit harmonic characteristics that are time-varying and stochastic in nature [204]. For inverter-based resources, including PV systems and battery energy storage, harmonic emissions depend on the operating points, control strategies, and prevailing grid conditions. Electric Vehicle (EV) chargers introduce additional uncertainty owing to variable connection times and charging profiles. Moreover, the background harmonic levels fluctuate as the system conditions change, complicating the assessment of the incremental harmonic contributions from individual sources. Dynamic harmonic source models are required to accurately capture time-varying behavior. Responsibility assignment methodologies should be extended to stochastic frameworks that incorporate uncertainty quantification and confidence intervals. In addition, online learning and adaptive modeling approaches should be investigated to enable the continuous updating of source characteristics as operating conditions evolve.

4.6.3. Lack of Standardized Responsibility Metrics

Despite extensive research efforts, no universally accepted metrics currently exist for quantifying harmonic responsibility. Existing studies have defined responsibility using diverse criteria, such as the harmonic emission level and harmonic severity indicator [125], current contribution [13,19,41], power contribution [205], voltage impact [19,206], and background harmonic distortion [73]. This lack of standardization introduces regulatory ambiguity, limiting the ability of utilities to consistently assign responsibility or enforce mitigation measures. Furthermore, different metrics can lead to significantly different responsibility allocations, raising concerns about fairness and transparency. Standardized harmonic responsibility metrics should be established through industry consensus. Future research should prioritize the exploration of equitable allocation methodologies that incorporate network topology, source location, and the overall impact on the system. Additionally, there is a need to formulate regulatory frameworks based on the rigorous and transparent quantification of responsibilities.

Table 11 clearly indicates that progress in wide-area harmonic monitoring and source identification is still hampered by a combination of technical, data, and operational challenges, most of which remain at an early or intermediate stage of maturity. The most pressing research needs are those that directly affect system-wide visibility and the ability to act on monitoring results. In particular, gaps in D-PMU coverage, difficulties in combining heterogeneous data sources, and a lack of computationally efficient frameworks stand out as major barriers to reliable wide-area deployments. Table 11 also highlights the critical need for more robust harmonic source attribution methods. Accurately assigning responsibility is especially challenging in modern networks with aggregated, time-varying, and stochastic sources driven by power electronic devices and DERs. These issues have a significant impact but are underdeveloped, making them strong candidates for near-term research. Meanwhile, limited training data and data quality concerns continue to restrict the performance of AI-based approaches, highlighting the importance of improved measurements and uncertainty-aware modeling. Taken together, the research priorities emphasize scalable, real-time, and data-integrated solutions that can operate within practical system constraints. Addressing these high-priority gaps is essential for enabling standardization, supporting regulatory frameworks, and achieving large-scale, real-world deployments of wide-area harmonic monitoring systems.

5. Future Research Directions

To effectively bridge the identified gaps, it is crucial to initiate coordinated research efforts across diverse technical fields. This section outlines key future research directions, systematically organized according to strategic priorities, as summarized in

Table 12. Future Research Directions for Data-Driven Harmonic Monitoring and Mitigation.

Theme	Research Focus	Key Ideas, Benefits, and Challenges
AI-Enhanced Harmonic Estimation	Physics-informed learning, multi-fidelity fusion, and sensor placement	High-rate D-PMU data can be combined with AI to overcome the limitations of sparse sensing and modeling. Promising directions include physics-informed neural networks that embed power system laws, the Bayesian fusion of D-PMU, AMI, and SCADA data, and active learning strategies for cost-effective D-PMU placement. These approaches improve accuracy and generalization but must address computational cost, topology changes, and asynchronous data.
Digital Twins and Learning-Based Control	Digital twins, reinforcement learning, and forecasting	Continuously synchronized digital twins enable the safe testing of harmonic mitigation strategies. Reinforcement learning can coordinate distributed active filters, whereas forecasting models can anticipate harmonic issues minutes to hours ahead. Together, they support proactive and adaptive mitigation. Key challenges include model fidelity, simulation-to-real transfer, safety guarantees, and uncertainty-aware decision making.
Harmonic Responsibility Assignment	Causal inference, blockchain, and game theory	Accurate and fair attribution of harmonic responsibility is essential for enforcement and incentive creation. Causal inference helps distinguish correlation from causation, cooperative game theory provides fairness guarantees, and blockchain offers transparent and auditable responsibility tracking. Scalability, privacy, and computational complexity remain open issues.
Advanced Measurement Technologies	Low-cost sensors and hybrid PMU–AMI devices	Dense monitoring can be achieved using low-cost harmonic sensors and hybrid devices that combine D-PMU functionality with AMI metering. Event-triggered high-rate measurements reduce data volume while improving visibility. Challenges include maintaining accuracy, managing communications, and meeting regulatory requirements.
Standards and Regulation	Metrics, data formats, and interoperability	Widespread adoption requires standardized harmonic responsibility metrics and interoperable D-PMU data formats. Extending existing standards (e.g., IEEE C37.118) to include harmonic phasors would reduce integration barriers and regulatory uncertainty, though stakeholder consensus and international alignment are nontrivial.
Cross-Cutting Themes	Uncertainty, explainability, privacy, and grid integration	Future solutions must quantify uncertainty, remain robust to imperfect data, and provide explanations that operators can trust. Privacy-preserving learning and tight integration with broader grid modernization efforts (ADMS, OMS, DERMS) are critical for real-world deployment and acceptance.

.

Roadmap and Priorities

Table 13. Roadmap of Key Research Directions for Wide-Area Harmonic Monitoring.

Research Direction	Time Horizon	Technical Feasibility	Impact on Wide-Area Monitoring	Priority	Key Stakeholders
Physics-informed neural networks for HSE	Near-term (1–2 years)	High	High	Critical	Universities, research labs, software vendors
Multi-fidelity data fusion frameworks	Near-term (1–2 years)	High	High	Critical	Utilities, H-PMU or D-PMU vendors, research institutions
Digital twin frameworks for power quality	Medium-term (2–4 years)	Medium	Very High	Critical	Utilities, software vendors, national laboratories
Active learning for H-PMU or D-PMU placement	Near-term (1–2 years)	High	Medium	High	Utilities, planning departments
Causal inference for responsibility assignment	Medium-term (2–4 years)	Medium	High	High	Regulators, utilities, research institutions
Reinforcement learning for active filter control	Medium-term (3–5 years)	Medium	Medium	Medium	Utilities, mitigation equipment vendors
Low-cost distributed harmonic sensors	Long-term (4–6 years)	Medium	High	Medium	Sensor manufacturers, utilities
Blockchain-based responsibility ledger	Long-term (5+ years)	Low	Medium	Low	Utilities, regulators, blockchain developers
Harmonic responsibility metrics standardization	Near-term (1–3 years)	High	High	Critical	IEEE, IEC, regulators, utilities
H-PMU or D-PMU data format and interoperability standards	Near-term (1–2 years)	High	High	Critical	IEEE, D-PMU vendors, utilities

Time Horizon: Near-Term = 1–2 years; Medium-Term = 2–4 years; Long-Term = 4+ years. Priority: Critical = Essential for wide-area monitoring deployment; High = Significant impact; Medium = Valuable but not essential; Low = Recommended but not essential. Technical Feasibility: Based on current technology readiness levels and anticipated development challenges.

outlines a proposed prioritized roadmap for future research, considering technical feasibility, potential impact, and projected time horizon. The roadmap highlights that the most critical initiatives are concentrated in the near term, with particular emphasis on AI-driven estimation, data fusion, and standardization. Looking ahead to the medium- and long-term horizons, the focus shifts towards system automation, control, and infrastructure, involving a diverse array of stakeholders from utilities, industry, and research organizations. These initiatives aim to enhance the accuracy and reliability of forecasting models while promoting interoperability across different platforms and datasets. Collaboration among stakeholders is vital to address technical challenges and ensure successful implementation. Continuous evaluation and adaptation of the roadmap are necessary to respond to emerging technologies and evolving industry requirements. Unlike earlier static models, this roadmap emphasizes ongoing assessment to keep pace with technological advances and industry shifts. Furthermore, the collaborative and adaptive approach distinguishes it from isolated or one-time implementation efforts.

6. Conclusions

This review provides a structured comparative assessment of harmonic source modeling approaches using a unified coverage and maturity framework. Based on the comparative analysis of 128 recent papers (2000–2026), the strengths, limitations, and applicability of each methodological paradigm are identified, leading to several key findings:

i

Classical/analytical and measurement-based methods remain the most mature and consistently validated approaches.

ii

Data-driven methods show the strongest growth but are associated with lower levels of validation realism.

iii

Application-oriented aspects—including real-time capability, wide-area applicability, and validation realism—exhibit moderate and uneven development, indicating that methodological advances are not yet fully aligned with deployment-oriented progress.

The results reveal a clear imbalance between methodological expansion and validation depth. Robustness analysis further confirms that these trends are stable, showing limited sensitivity to leave-one-out and perturbation tests.

Based on these findings, future research should prioritize improving validation realism through the use of real-world data, large-scale evaluation, and field-level validation. Bridging the gap between data-driven approaches and operational deployments remains a key challenge, requiring integration with physical constraints and system-level considerations. Further work is needed to develop scalable wide-area monitoring frameworks suitable for modern power systems. Aligning methodological innovation with practical applicability will be essential to ensure that advances in modeling translate into reliable, deployable solutions.