{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T17:02:22Z","timestamp":1770742942009,"version":"3.49.0"},"reference-count":42,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,3,23]],"date-time":"2025-03-23T00:00:00Z","timestamp":1742688000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Due to their crucial impacts on the stability of the power system and their significant power demand, industrial loads, with their symmetrical and asymmetrical properties, have been gaining more recognition in the composite load modeling field. The established composite load model, known as the complex load (CLOD) model and used in commercial simulators (Power System Simulation for Engineering (PSS\u00aeE) and PowerWorld Simulator), has been used to represent composite loads efficiently. This model has a limited number of parameters combined with high accuracy. In the literature, the mathematical representation of this model is incomplete due to the complexity of some components of this model. This paper proposes a detailed mathematical representation of the CLOD model to enhance its capability and efficiency in capturing the dynamic response. Heuristic and regression techniques are utilized to estimate and tune the parameters of the proposed model. Compared with existing composite models, the proposed model requires a minimum set of parameters and low computational demand while ensuring accuracy with ease of implementation in large-scale industrial circuits. For model verifications, the output of the proposed model is compared with the output from the PSS\u00aeE model under different symmetric and asymmetric load distribution structures representing common customer classes, including residential, commercial, and industrial loads.<\/jats:p>","DOI":"10.3390\/sym17040481","type":"journal-article","created":{"date-parts":[[2025,3,24]],"date-time":"2025-03-24T13:48:20Z","timestamp":1742824100000},"page":"481","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Asymmetric Dynamic Modeling and Parameter Evaluation of Complex Load Model for Power System Stability Analysis"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-3729-128X","authenticated-orcid":false,"given":"Ibrahim","family":"Alzubi","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, Faculty of Engineering, Jordan University of Science and Technology, Irbid 22110, Jordan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3960-7534","authenticated-orcid":false,"given":"Saher","family":"Albatran","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Faculty of Engineering, Jordan University of Science and Technology, Irbid 22110, Jordan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7593-7787","authenticated-orcid":false,"given":"Issam A.","family":"Smadi","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Faculty of Engineering, Jordan University of Science and Technology, Irbid 22110, Jordan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2427-5829","authenticated-orcid":false,"given":"Salman","family":"Harasis","sequence":"additional","affiliation":[{"name":"Department of Electrical Power and Mechatronics Engineering, Tafila Technical University, Tafila 66110, Jordan"}]},{"given":"Yazan","family":"Alsmadi","sequence":"additional","affiliation":[{"name":"Department of Engineering, Computing and Mathematical Sciences, Lewis University, Romeoville, IL 60446, USA"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5986","DOI":"10.1109\/TSG.2017.2700436","article-title":"Load modeling\u2014A review","volume":"9","author":"Arif","year":"2017","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Lv, Z., Jia, B., Song, Z., Li, H., Zhou, S., and Li, Z. (2025). Stability Control Method Utilizing Grid-Forming Converters for Active Symmetry in the Elastic Balance Region of the Distribution Grid. Symmetry, 17.","DOI":"10.3390\/sym17020263"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1372","DOI":"10.1109\/TPWRD.2013.2285096","article-title":"Experimental determination of the ZIP coefficients for modern residential, commercial, and industrial loads","volume":"29","author":"Bokhari","year":"2013","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Deng, C., Dai, L., Chao, W., Huang, J., Wang, J., Lin, L., Qin, W., Lai, S., and Chen, X. (2025). An Advanced Spatio-Temporal Graph Neural Network Framework for the Concurrent Prediction of Transient and Voltage Stability. Energies, 18.","DOI":"10.3390\/en18030672"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Chassin, F.S., Mayhorn, E.T., Elizondo, M.A., and Lu, S. (2011, January 4\u20136). Load modeling and calibration techniques for power system studies. Proceedings of the 2011 North American Power Symposium, Boston, MA, USA.","DOI":"10.1109\/NAPS.2011.6024878"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Bai, W., Zhu, J., Zhao, J., Cai, W., and Li, K. (2022). An Unsupervised Multi-Dimensional Representation Learning Model for Short-Term Electrical Load Forecasting. Symmetry, 14.","DOI":"10.3390\/sym14101999"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3304","DOI":"10.1109\/TSG.2016.2630027","article-title":"Robust time-varying load modeling for conservation voltage reduction assessment","volume":"9","author":"Zhao","year":"2016","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Xiao, C., Ren, Y., Cao, Q., Cheng, R., and Wang, L. (2024). Propagation Mechanism and Suppression Strategy of DC Faults in AC\/DC Hybrid Microgrid. Processes, 12.","DOI":"10.3390\/pr12051013"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/j.epsr.2007.02.003","article-title":"Dynamic load modelling based on measurements in medium voltage distribution network","volume":"78","year":"2008","journal-title":"Electr. Power Syst. Res."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2204","DOI":"10.1109\/TPWRS.2007.907582","article-title":"Effect of load models in distributed generation planning","volume":"22","author":"Singh","year":"2007","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Dimitrakakis, G.S., Georgakas, K.G., Topalis, E.S., and Vovos, P.N. (2024). Grid Quality Services from Smart Boilers: Experimental Verification on Realistic Scenarios for Micro-Grids with Demand-Side Management Oriented to Self-Consumption. Energies, 17.","DOI":"10.3390\/en17092096"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"AlMuhaini, M., Yahaya, A., and AlAhmed, A. (2023). Distributed Generation and Load Modeling in Microgrids. Sustainability, 15.","DOI":"10.3390\/su15064831"},{"key":"ref_13","unstructured":"Kundur, P.S., and Malik, O.P. (2022). Power System Stability and Control, McGraw-Hill Education."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2279","DOI":"10.1109\/TPWRS.2019.2953757","article-title":"Modeling and experimental validation of power electronic loads and DERs for microgrid islanding simulations","volume":"35","author":"Roos","year":"2019","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1590","DOI":"10.3390\/smartcities5040081","article-title":"Power Quality Analysis by H-Bridge DSTATCOM Control by Icos\u03b8 and ESRF SOGI-FLL Methods for Different Industrial Loads","volume":"5","author":"Islavatu","year":"2022","journal-title":"Smart Cities"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Shin, K., Ko, K., and Hwang, J. (2025). The Development and Characteristics of an In-Wheel Assembly Using a Variable Speed-Reducing Device. World Electr. Veh. J., 16.","DOI":"10.3390\/wevj16020092"},{"key":"ref_17","unstructured":"Balu, C., and Maratukulam, D. (1994). Power System Voltage Stability, McGraw-Hill."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/S0378-7796(00)00103-6","article-title":"A third order model for the doubly-fed induction machine","volume":"56","author":"Carrillo","year":"2000","journal-title":"Electr. Power Syst. Res."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1015","DOI":"10.35833\/MPCE.2019.000296","article-title":"Mathematical representation of WECC composite load model","volume":"8","author":"Ma","year":"2020","journal-title":"J. Mod. Power Syst. Clean Energy"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1109\/59.221270","article-title":"Nonlinear dynamic load models with recovery for voltage stability studies","volume":"8","author":"Hill","year":"1993","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1868","DOI":"10.1109\/59.331443","article-title":"Power system dynamic load modeling using artificial neural networks","volume":"9","author":"Ku","year":"1994","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3038","DOI":"10.1109\/TPWRS.2012.2231969","article-title":"International industry practice on power system load modeling","volume":"28","author":"Milanovic","year":"2012","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Kosterev, D., Meklin, A., Undrill, J., Lesieutre, B., Price, W., Chassin, D., Bravo, R., and Yang, S. (2008, January 20\u201324). Load modeling in power system studies: WECC progress update. Proceedings of the 2008 IEEE Power and Energy Society General Meeting\u2014Conversion and Delivery of Electrical Energy in the 21st Century, Pittsburgh, PA, USA.","DOI":"10.1109\/PES.2008.4596557"},{"key":"ref_24","unstructured":"Western Electricity Coordinating Council (2015). WECC Dynamic Composite Load Model (CMPLDW) Specifications, WECC. WECC Tech. Rep."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"5441","DOI":"10.1109\/TPWRS.2021.3078671","article-title":"Parameter reduction of composite load model using active subspace method","volume":"36","author":"Ma","year":"2021","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1109\/TPWRS.2018.2865966","article-title":"SVM-based parameter identification for composite ZIP and electronic load modeling","volume":"34","author":"Wang","year":"2018","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_27","unstructured":"Guo, S., and Overbye, T.J. (2012, January 24\u201325). Parameter estimation of a complex load model using phasor measurements. Proceedings of the 2012 IEEE Power and Energy Conference at Illinois, Champaign, IL, USA."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Hoshyarzadeh, A.S., Zareipour, H., Keung, P.-k., and Ahmed, S.S. (2019, January 11\u201314). The impact of CLOD load model parameters on dynamic simulation of large power systems. Proceedings of the 2019 IEEE International Conference on Environment and Electrical Engineering and 2019 IEEE Industrial and Commercial Power Systems Europe (EEEIC\/I&CPS Europe), Genova, Italy.","DOI":"10.1109\/EEEIC.2019.8783527"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"105983","DOI":"10.1016\/j.ijepes.2020.105983","article-title":"The impact of large-scale dynamic load modeling on frequency response in the US Eastern Interconnection","volume":"120","author":"Bennett","year":"2020","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_30","unstructured":"Li, S., Liang, X., and Xu, W. (2017, January 6\u201311). Dynamic load modeling for industrial facilities using template and PSS\/E composite load model structure CLOD. Proceedings of the 2017 IEEE\/IAS 53rd Industrial and Commercial Power Systems Technical Conference (I&CPS), Niagara Falls, ON, Canada."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1109\/TPWRD.2014.2301219","article-title":"Estimation of composite load model parameters using an improved particle swarm optimization method","volume":"30","author":"Regulski","year":"2014","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"4331","DOI":"10.1109\/TSG.2020.2988171","article-title":"Two-stage WECC composite load modeling: A double deep Q-learning networks approach","volume":"11","author":"Wang","year":"2020","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Prabpal, P., Kongjeen, Y., and Bhumkittipich, K. (2021). Optimal Battery Energy Storage System Based on VAR Control Strategies Using Particle Swarm Optimization for Power Distribution System. Symmetry, 13.","DOI":"10.3390\/sym13091692"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Liao, L., Leung, V.C.M., Li, Z., and Chao, H.-C. (2021). Genetic Algorithms with Variant Particle Swarm Optimization Based Mutation for Generic Controller Placement in Software-Defined Networks. Symmetry, 13.","DOI":"10.3390\/sym13071133"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1016\/j.simpat.2010.01.003","article-title":"Power transformer differential protection using neural network Principal Component Analysis and Radial Basis Function Neural Network","volume":"18","author":"Tripathy","year":"2010","journal-title":"Simul. Model. Pract. Theory"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"5407","DOI":"10.1109\/TSG.2020.3008730","article-title":"WECC composite load model parameter identification using evolutionary deep reinforcement learning","volume":"11","author":"Bu","year":"2020","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_37","unstructured":"Siemens (2013). \u201cProgram Application Guide\u201d, PSS\u00aeE Users\u2019 Manual, Siemens."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Duan, J., Bao, Y., Zhang, G., Wang, X., Jiang, P., Niu, W., Zhang, H., Zhen, W., Xia, Y., and Song, R. (2025). Modeling and Simulation Analysis of Three-Phase Saturable Transformers: A Study on the Effects of Geomagnetically Induced Current on Transformers. Energies, 18.","DOI":"10.3390\/en18040824"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"107153","DOI":"10.1016\/j.epsr.2021.107153","article-title":"Determination of the saturation curve of power transformers by processing transient measurements","volume":"195","author":"Canal","year":"2021","journal-title":"Electr. Power Syst. Res."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1302","DOI":"10.1109\/59.466523","article-title":"Standard load models for power flow and dynamic performance simulation","volume":"10","author":"Price","year":"1995","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_41","unstructured":"(2020). Voltage Ratings for Electric Power Systems and Equipment (60 Hz) (Standard No. ANSI C84.1-2020)."},{"key":"ref_42","unstructured":"The MathWorks, Inc. (2024, October 08). Curve Fitting Toolbox. Natick, Massachusetts, United States. Available online: www.mathworks.com\/products\/curvefitting.html."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/4\/481\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:58:45Z","timestamp":1760029125000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/4\/481"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,23]]},"references-count":42,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,4]]}},"alternative-id":["sym17040481"],"URL":"https:\/\/doi.org\/10.3390\/sym17040481","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,23]]}}}