Load modeling techniques in distribution networks: a review

Introduction

Load modeling is a process of estimating a power consumption of a typical infrastructure, it can be of commercial, agricultural, industrial or residential infrastructure [1-5]. Whereas, identification means the process of developing a mathematical relation between different parameters of interest of a dynamic system obtained by either observation, prior knowledge or both [6,7]. The representation can be in form of mathematical equations or graphical relationships. Load modeling and identification is an important aspect in area of stability analysis, planning, monitoring, control and protection of power system [10,8,9]. Accurate load model is required in design and adjustment of transmission and distribution networks, design for protective devices such as circuit breakers, relays and also for the control, monitoring and analysis of the system [11-13]. Electric loads are dynamic and extremely nonlinear in nature, they are therefore difficult to be optimally model. Generally, there are two approaches in load modeling reported in many literatures, component based modeling and measurement based modeling [1,12,14,15,3].

Component based load modeling approach need the physical individual loads information to form an analytical mathematical function that represents the relationship between the system voltages, frequency, real and reactive power consumed by the load [16-18]. This approach however, cannot give the actually time-variant behavior of the load composition, but has advantages of not requiring field measurements, it is also easier to adapt to different systems and conditions. Another advantage is that once it is developed it can be used for the full system life, only the load class mix data must to be updating [19,20]. In contrary, measurement based load modeling approach uses of field data, obtainable from sensor installed at load Bus of which the model is intend to developed, load is well known to be time-variant and nonlinear; for these reasons therefore, the measurement based load model overtakes the component based load model [21].

Load models are classified into two main categories: static and dynamic models. Static models express the real and reactive power at any instant of time as functions of bus voltage magnitudes and frequency. This category of model can be used to represent static loads e.g., resistive loads. In contrast, dynamic load model expresses active and reactive powers as a function of voltage and time. Another model is composite load model which combine the static and the dynamic for more accurate system representation [12,22,23]. There are many type of loads in power systems some are static while some are dynamic in nature, normally we have lighting, heating and cooling devices, audio and audio-visual systems, converters etc. the effect of distribution lines and shunt capacitors connected to the distribution system aggregated with the typical consumption are usually modeled to represents the third tier (Distribution System) of power system [24].

Majority of power system faults are not originated by instability, but by unanticipated protection operation which heavily depends on actual load at a given time of operation. Also postmortem analysis of power system disturbances always reveals discrepancies between measured and simulated behavior [22,24]. Accurate load modeling is critical such that the measured and simulated will represent one another for acceptability of the model. Exact load model is required for voltage stability studies, angular stability studies, power system planning, design and reconfiguration of transmission and distribution networks. Load modeling is very important in attempt to address the emerging issues arising in the area; the increase penetration of new types of load as well as the advancement in measurement devices such as Phasor Measurement Unit (PMU), Supervisory Control and Data Acquisition (SCADA), and Smart Meter (SM) pose the field to regain attention globally [17,9]. Distribution networks were mainly loads in the past, now they are transforms to active in which distributed generations are incorporated in them, future Distribution Networks (DNs) are desired to be smart, and for the DN system to be smart there is a need of accurate load representation of the active distribution networks [19]. A number of attempts are made to come up with accurate load models for static, dynamic, and even composite loads using different methods but yet confirmed challenging. Most of the techniques suffer from complexity, majority miscarries active distribution networks while some considered traditional Static models or dynamic only.

Load Models nad Types of Load Models

Model is just a set of mathematical equivalences, analytical or equivalent circuit based, that describes input-output relationship of a system, while load is any electrical component, device or equipment that is connected to supply in parallel, with intension to consume active power [2,25]. In load modeling sense, the representation is given in terms of voltage and frequency values as inputs of the model, while real and reactive powers are set as the output of the model mostly captured at a Load bus. Because of load distribution and diversity of it, different substitutes have been proposed channel out the time for their representation and their resolution [15,26]. The following categorized the different types of load modeling:

Static Load Model

Static load model is not a time dependent model, it always represents the real and reactive power as a function of voltage and frequency at any instant of time [27,28]. The static load models have been applied for a lengthy time to represent static load components, such as resistive and lighting loads, and also to estimate dynamic loads components [18,29-32]. The models are expressed in a polynomial or an exponential form, These types of models are mostly use in analysis of equilibrium condition of power systems [33,34]. Descriptions of some of these models are given as follows:

Constant Impedance (Z), Constant Current(I) and Constant Power (P) (ZIP Model)<italic id="italic-1"><bold id="bold-1"> </bold></italic>

Static features of load can be categorized into constant impedance, constant current and constant power load, subject to the power relation to the voltage. For a constant impedance load, the power dependence on voltage is quadratic, for a constant current it is linear, and for a constant power, the power has no relation with changes in voltage. This type of model is also known as Polynomial Model [11]. Figure 1 shows a typical representation of ZIP model. The Model can be described by the equations (1) and (2).

fig-2ffe75d72c1fc4fd225ec7f587aeac9c Polynomial Model/ZIP Model Equivalent Circuit

\begin{equation} P_{A}=P_{n}\left ( \alpha _{z}\left [ \frac{V_{A}}{V_{n}} \right ]^{2}+\alpha _{z}\left [ \frac{V_{A}}{V_{n}} \right ]^{2}+\alpha _{p} \right ) \tag{1} \end{equation}

\begin{equation} Q_{A}=Q_{n}\left ( \beta _{z}\left [ \frac{V_{A}}{V_{B}} \right ]^{2}+\beta _{t}\left [ \frac{V_{A}}{V_{n}} \right ]^{2}+\beta _{p} \right ) \tag{2} \end{equation}

where: \( P_{A} \), \( Q_{A} \) are respective real and reactive powers of a given phase, \( P_{n} \), \( Q_{n} \) are active and reactive power of the load at the nominal voltage \( V_{n} \); \( V_{A} \) is a phase voltage; \( \alpha_{z} \), \( \alpha_{t} \), \( \alpha_{p} \) and \( \beta_{z} \), \( \beta_{t} \), \( \beta_{p} \) are proportions of constant impedance, current, and power components of active and reactive power of the total static load respectively [35,36].

 Exponential Model

Exponential model relates voltage and power parameters of a load bus by exponential mathematical equations. It has few parameters and is usually use to represent mixed load [14,23]. In the equation, numerous components with different exponents can be encompassed. The model equations are expressed as follows:

\begin{equation} P=P_{0}\left ( \frac{v}{v_{0}} \right )^{np} \tag{3} \end{equation}

\begin{equation} Q=Q_{0}\left ( \frac{v}{v_{0}} \right )^{nq} \tag{4} \end{equation}

where: \( P_{0} \) and \( v_{0} \) are the initial values of active power and voltage respectively, \( np \) and \( nq \) are parameters that can be adjusted to get the best representation of the voltage dependence of the load, \( Q_{0} \) is the initial value of the reactive power [11,2].

 Frequency Dependent Model

Frequency dependency of the load is not very significant [37]. But can also be considered in formulation of a load model. The model is derived from ZIP or Exponential model by multiplying the frequency defendant factor with the ZIP equation or polynomial equations. The frequency defendant factor is represented by equation (5):

\begin{equation} f_{factor}\left ( 1+\alpha \Delta f \right ) \tag{5} \end{equation}

where: \( \Delta f \) is the frequency deviation from 50Hz (normal value), and is the frequency sensitivity parameter [14].

 Dynamic Load Model

A dynamic load model is time dependent, it states the relationship of voltage and if necessary frequency values, active and reactive power at any point of time, as a function of voltage and the frequency time history, including normally the present moment. Dynamic model is particularly important in voltage and angular stability studies [14,28]. Induction Motor (IM) model is the most common dynamic load model used (almost 70% of the total energy supply by utilities are consume by electric motors and large portion of this are IMs); the model is obtained from the circuit of figure 2 and represents the real and reactive power as a function of the previous and current voltage and frequency of the load bus. Exponential recovery load model can also be used to represent dynamic load model [38]. The model is generally used to represents loads that gradually recover over time period and are developed as nonlinear first order differential equations as depicted in equations (6) to (9).

\begin{equation} T_{p}\frac{dx_{p}}{d{t}}=-x_{p}+p_{0}\left ( \frac{v}{v_{0}} \right )^{N_{ps}}-p_{0}\left ( \frac{v}{v_{0}} \right )^{N_{pt}} \tag{6} \end{equation}

\begin{equation} p_{d}=x_{p}+p_{0}\left ( \frac{v}{v_{0}} \right )^{N_{pt}} \tag{7} \end{equation}

\begin{equation} T_{p}\frac{dx_{q}}{d{t}}=-x_{p}+Q_{0}\left ( \frac{v}{v_{0}} \right )^{N_{qs}}-Q_{0}\left ( \frac{v}{v_{0}} \right )^{N_{qt}} \tag{8} \end{equation}

\begin{equation} Q_{d}=x_{q}+Q_{0}\left ( \frac{v}{v_{0}} \right )^{N_{qt}} \tag{9} \end{equation}

where \( x_{p} \) and \( x_{q} \) are state variables associated with real and reactive power dynamics, \( T_{p} \) and \( T_{q} \) are time constants of the exponential recovery response, \( N_{ps} \) and \( N_{qs} \) are exponents related to the steady-state load response, \( N_{pt} \) and \( N_{qt} \) are exponents related to the transient load response Arif et al. [14]. Equivalent circuit diagram for this type of model can be represented as in Figure 2.

fig-aa0069763c692bcd0a9e9b2c9a03fea9 Equivalent Circuit Diagram of IM Model

Composite Load Model

Composite load model is another model that consists of both static as well as dynamic load components to formulate a model. Literatures have shown that composite load models provide more accurate response than the statics or dynamic models alone [12,39]. A common composite load model is the combine ZIP and IM, figure 3 shows the representative circuit diagram of composite load model (ZIP and IM).

fig-6742885e0d4d9d4362e29dcfec764dcb Composite Load Model Equivalent Circuit Diagram

The static part is represented by equations (1) to (5) while the dynamic part is represented by equations (6) to (9). Any typical load center of a power system comprises jointly static and dynamic combinations of loads and that is the reason why composite load model give more accurate representation of the loads in distribution systems.

 Distribution System

Distribution Network (DN) is a branch of power system infrastructure that convey electricity from high-voltage transmission network and delivers it to end user, in the process; the high voltages from transmission network are step down to medium voltage via distribution transformers suitable for large industries. Further step down is been done to accommodate residential and commercial consumers at lower level voltages [40]. In the past, distribution networks ware mainly passive, meaning that they are only a means of energy delivery to the end uses (unidirectional flow). Advancement reach to a time that DNs are transform to active, i.e. they involve a number of Distributed Generations (DGs) connected in them to improve system reliability, availability and quality of supply [19]. Future DNs are desired to be smart, in which they will support bidirectional power flow and communication infrastructure will be incorporated to the Active Distribution Networks (ADNs) available today [41,42]. The present ADN comprises different types of loads ranging from statics, dynamics and combination of the statics and the dynamic (composite). The aggregation of these loads, together with shunt active capacitors, line effects, and grid connected DGs formed the aggregate loads in a particular load bus. Load modeling considering DN as a whole is particularly important in voltage and angular stability studies and also in analysis of equilibrium operating condition of power system [4,43].

 Power Identification

Load modeling involves two stages, the choice of load model structure and the valuation of load model parameter [22].

i. Choice of load model structure: Choice of load model structure has to do with the load bus of interest. Power system operators are mainly interested on the buses within their control area. Planners and researchers uses IEEE standard test Systems to developed a concept for planning purposes while in system analysis all or any of the above mention structure can be useful defending on the nature of the problem on ground [33,44].

ii. Parameter identification: In parameter identification of load modeling, the problem is curve fitting/estimation type, which is trying to represent the characteristics of a load bus. The process can be accomplished by two different approaches as shown in the Figure 4. The component based and measurement base estimation [13-15,45,46].

fig-02c21c317750874e4c4f192c41dc18d5 Load Parameter Identification Approaches

Component Based Approach

The Component based approach needs the information of individual loads in a substation based on load class (i.e. residential, agricultural, commercial, industrial and special) gathered together to identify the load parameter [10,15]. In this situation each of the composition is replaced using static or dynamic representation based on the load type known from experiments. Loads are usually classified by utility companies as residential, commercial, industrial, Agricultural and special [2,47,48]. This is in consideration of the load consumptions magnitude, time variant of utilization and purpose. Determination of individual load consumption for parameter identification is a serious challenging task, if not impossible, the mission is accomplished by laboratory experiment test of each appliance and later aggregated their values. The errors associated with this method are due to changes in weather, geographical location and experimental errors among others. For these reasons therefore, component based approach which cannot actually capture the time variant nature of load is considered imperfect [21,49].

 Measurement Based Approach

This approach makes use of historical measurement data obtainable from different measurement devices usually installed at load bus substations. Devices such as Smart Meters (SM), Digital Fault Recorder (DFR), Power Quality Monitors (PQM) and Phasor Measurement Unit (PMU) are now used to capture network data in real time at both low and medium voltage levels [13]. The advantages of this method are that; the model is developing based on actual real time scenario, and there is no need of having deep knowledge of individual loads. Basically there are two techniques reported for parameter identification in measurement based: the statistical and the metaheuristics methods as seen in Figure 4 [10,11]. The statistical method is actually an analytical approach which is characterized with computational error. Although it is more preferred when compared with component based in terms of both accuracy and simplicity. These techniques include; Least Square (LS) method, Vector Fitting (VF) technique, Weighted LS (WLS), Kaman’s filter among others. The evolutions of metaheuristics techniques opens another window for load modeling techniques as they perform better in terms of both accuracy and reduction of computational time [12].

The whole process of measurement based approach of load modeling can be brief as follows:

identification of model structure (i.e. Load Bus)

data accusation accomplished with a measurement device

formulate a load model

provide an optimization technique that will minimized cost function and thereby identifying the load parameter

evaluations of the cost function by testing the results

model validation

The process above is also described in Figure 5. Measured voltage (v) and if necessary with corresponding frequency (f) values are uses as input to the model, the model use this information to estimate active and reactive powers e and Q e respectively. The estimated powers (real and reactive) are then compared with the real load measurement Pm and Q m with the aim of minimizing the error function of equation (10). This is where the optimization algorithms such as Particle Swarm Optimization (PSO) algorism, Improve PSO algorism, Genetic Algorithm (GA) etc. plays a role [12,14]. Measurement base approach has a better performance in reflecting the load characteristics in dynamic situations [21,50]. Loads are well known to be dynamic and time variant; consequently, this might be the reason why the approach is being widely used.

\begin{equation} f_{e}=\frac{1}{N}\sum \left ( P_{m}-P_{e} \right )^{2}+\left ( Q_{m}-Q_{e} \right )^{2} \tag{10} \end{equation}

fig-c53fe234ad0526301a5686fda446a9a4 Block Diagram of Load Parameter Estimation

Research Trends and Future Research Direction

Load modeling has been identified as an important aspect in power system studies, the area is gaining more attention with the penetration of new types of load, transformation of distribution networks from passive to active and certainly it will continue to attract research attention as future distribution network will be smart.

Research Trend

load modeling and identification is old as well as new area of research, it is old because it has been an area in which system equilibrium condition is determine via static models [20,43]. It is also applied in stability studies via both dynamic and composite models [51]. Because of serious innovations of electronics devices, increase in renewable energy penetration and DG placement in the distribution network it become a new area of research as well [13]. Attempts have been made by many researchers channel out time, and accuracy to come up with optimal load model at different stages. Unfortunately, it has been discovered challenging. Table 1, summarized some accessible research effort done in the area recently.

table-wrap-9229ee55ccd02f0ee87ed0956492fae1 Summary of Load Modeling in the Recent Literature

Author(s) Identification technique Types of Model Network Type Shortcomings
Hua et al. [52] Statistical/Transfer Function (TF) Dynamic AND TF does not take account of initial conditions of the system
Rouhani & Abur [28] Statistical/Kalman’s Filter (KF) Dynamic Passive Network (PN) Small steady state error associated with KF
Vignesh et al. [36] Statistical/ Variable rejection method Dynamic PN ZIP model cannot capture the time varying nature of loads
Kontis et al. [3] Statistical / Vector Fitting Dynamic PN Computational intensive requirement in addition to Multiple local optimums
Kontis et al. [33] Statistical /TF Dynamic PN TF does not take account of initial conditions of the system
Wang [53] Statistical /dynamic equations Dynamic PN Exhibits high amount of error with small convergence speed
Jahromi & Ameli [12] Metaheuristics /GA Composite PN Slow convergence characteristics
Saviozzi et al. [54] ANNs Dynamic PN Absent of temporal connection in ANNs
Zheng et al. [15] RNNs Composite ADN RNNs does not perform well when the Operating Condition (OC) are change far from the original OC

Load, actually is time- dependent, hence measurement based approach clearly outperforms component based approach. It can be seen from table 1, that; most of the recent works uses measurement /statistical techniques. However, the most recent researches use Neural Networks (NN) identification techniques for their advance capabilities and in an attempt to tradeoff between accuracy and time consumption. Besides, NN do not have to be retrained if there is change in the load consumption [54,55]. (Azmy et al., 2004; Saviozzi et al., 2019). Static models are succeeded by dynamic and composite models, at the same time, active distribution networks are considered by Zheng et al. [15] and Hua et al. [52] in the survey. Passive Networks (PNs) are considered in most cases probably due to their easy access since ADNs are in their developing stage [19].

 Areas of Future Research Work

Disturbances in power systems are naturally unbalanced, but most of the existing loads modeling methods are approximated as balanced disturbance, therefore there is a need to have an extensive investigation to the unbalanced situations. More search is required to develop improve methods of performing load modeling using online real time data, so that it can accurately capture the seasonal and geographical variations of the loads. In order to overcome the shortcoming associated with RNNs when the operating conditions are change far away from the original operating situation an effective technique is required for searching the threshold distance for good performance. The capability of Power System Computer Aided Design (PSCAD) software to interface with MATLAB/SIMULINK offers another idea of developing a link Library based PSCAD- RNN model [15,56]. Frequency dependency on load seems to be very small and mostly ignored in formulation of load models, closer look should be done in future to established whether it can or not be ignored. In the future, other machine learning techniques should be tested especially Support Vector Machine (SVM) as it perform excellent and demonstrate higher accuracy than any other machine learning in other areas of research [21,57,58]. Finally, as DNs are transformed from passive to active the research should be directed in such manner.

 Conclusion

In this paper, load modeling and identification techniques are critically reviewed. Detailed states of the art in the area are discussed and finally new approaches to the problems are pointed out. In load modeling and identification, a measurement based approaches are recommended as load is well known to be time variant and nonlinear. Also, new devices such as PMUs, SCADA and SMs are currently available. Metaheuristics optimization methods are considered superior over statistical methods in terms of accuracy and also ADNs in load modeling would be more current to consider than ordinary passive networks [57,59,60].

 655 2 661 April 17 2002 doi.org/10.1109/61.997955 Chang Rung-Fang Leou Rong-Ceng Lu Chan-Nan IEEE Transactions on Power Delivery Distribution transformer load modeling using load research data CIGRE SC C4 COLLOQUIUM: Fusion of Lightning Research and Practice for Power System in the Future Hakodate, Japan 10 October 2012 Dong Z. Y. Borghetti A. Yamashita K. Gaikwad A. Pourbeik P. Milanović J. V. CIGRE WG C4.065 Recommendations on Measurement Based and Component Based Load Modelling Practice 1 01 338-351 33 2018 10.1109/tpwrs.2017.2697004 Kontis Eleftherios O. Papadopoulos Theofilos A. Chrysochos Andreas I. Papagiannis Grigoris K. IEEE Transactions on Power Systems Measurement-Based Dynamic Load Modeling Using the Vector Fitting Technique 2017 3rd International Conference on Power Generation Systems and Renewable Energy Technologies (PGSRET) 04 2017 10.1109/pgsret.2017.8251791 Shafiei Mehdi Nourbakhsh Ghavameddin Ledwich Gerard Femando Tyrone Iu Herbert Arefi Ali 2017 3rd International Conference on Power Generation Systems and Renewable Energy Technologies (PGSRET) Dynamic load modelling using measured data in distribution networks 21 405-410 45 2012 10.3182/20120902-4-fr-2032.00072 Yamashita K Djokic S. Matevosyan J. Resende F.O. Korunovic L.M. Dong Z.Y. Milanovic J.V. IFAC Proceedings Volumes Modelling and Aggregation of Loads in Flexible Power Networks – Scope and Status of the Work of CIGRE WG C4.605 Courier Corporation 2009 Norton J. P. An Introduction to Identification International Conference on Power System Technology (POWERCON 2000) null 10.1109/icpst.2000.900024 Zhu S.Z. Dong Z.Y. Wong K.P. Wang Z.H. PowerCon 2000. 2000 International Conference on Power System Technology. Proceedings (Cat. No.00EX409) Power system dynamic load identification and stability 2015 IEEE Power & Energy Society General Meeting 07 2015 10.1109/pesgm.2015.7286541 Braunstein Sergio Halpern Bretas Newton Geraldo Rossoni Aquiles Bretas Arturo 2015 IEEE Power & Energy Society General Meeting Bad data analysis in distribution state estimation considering load models 3 08 1276-1283 21 2006 10.1109/tpwrs.2006.876700 Choi B.-K. Chiang H.-D. Li Y. Li H. Chen Y.-T. Huang D.-H. Lauby M.G. IEEE Transactions on Power Systems Measurement-Based Dynamic Load Models: Derivation, Comparison, and Validation 5 09 2180-2188 29 2014 10.1109/tpwrs.2014.2301949 Collin Adam J. Tsagarakis George Kiprakis Aristides E. McLaughlin Stephen IEEE Transactions on Power Systems Development of Low-Voltage Load Models for the Residential Load Sector Boston, MA, USA 4 August 2011 10.1109/NAPS.2011.6024878 Chassin Forrest S. Mayhorn Ebony T. Elizondo Marcelo A. Lu Shuai 2011 North American Power Symposium Load modeling and calibration techniques for power system studies 05 82-91 158 2018 10.1016/j.epsr.2017.12.023 Jahromi Mansour Eshragh-Niay Ameli Mohammad Taghi Electric Power Systems Research Measurement-based modelling of composite load using genetic algorithm 01 15 08 4069-4077 67 2019 10.1109/tsp.2019.2926023 Zhang Liang Wang Gang Giannakis Georgios B. IEEE Transactions on Signal Processing Real-Time Power System State Estimation and Forecasting via Deep Unrolled Neural Networks 6 11 5986-5999 9 2018 10.1109/tsg.2017.2700436 Arif Anmar Wang Zhaoyu Wang Jianhui Mather Barry Bashualdo Hugo Zhao Dongbo IEEE Transactions on Smart Grid Load Modeling—A Review 01 112-124 166 2019 10.1016/j.epsr.2018.09.006 Zheng Chao Wang Shaorong Liu Yilu Liu Chengxi Electric Power Systems Research A novel RNN based load modelling method with measurement data in active distribution system 3 08 1622-1630 20 2005 10.1109/tpwrs.2005.852123 Espinoza M. Joye C. Belmans R. DeMoor B. IEEE Transactions on Power Systems Short-Term Load Forecasting, Profile Identification, and Customer Segmentation: A Methodology Based on Periodic Time Series 3 09 1571-1572 3 2012 10.1109/tsg.2012.2198314 Stephen Bruce Galloway Stuart J. IEEE Transactions on Smart Grid Domestic Load Characterization Through Smart Meter Advance Stratification Tasić D. J. U. IEEE Transactions on Smart Grid The Influence of Static and Dynamic Load Characteristic on Voltage Collapse in Electrical Power System 07 4 04 501 10 2017 10.3390/en10040501 Kazmi Syed Ali Abbas Shahzad Muhammad Khuram Khan Akif Zia Shin Dong Ryeol Energies Smart Distribution Networks: A Review of Modern Distribution Concepts from a Planning Perspective 1 180-187 3 1988 10.1109/59.43196 Price W.W. Wirgau K.A. Murdoch A. Mitsche J.V. Vaahedi E. El-Kady M. IEEE Transactions on Power Systems Load modeling for power flow and transient stability computer studies San Diego, CA, USA 22 July 2012 10.1109/PESGM.2012.6344939 Hou Jia Xu Zhao Dong Zhao Yang 2012 IEEE Power and Energy Society General Meeting Measurement-based load modeling at distribution level with complete model structure X Symposium of Specialists In Electric Operational and Expansion Planning Brasil 21 May 2006 Hiskens Ian A. Significance of Load Modelling in Power System Dynamics 1 61-70 22 2009 10.2298/fuee0901061k Korunovic Lidija Stojanovic Dobrivoje Facta universitatis - series: Electronics and Energetics Dynamic load modeling of some low voltage devices 2012 47th International Universities Power Engineering Conference (UPEC) 09 2012 10.1109/upec.2012.6398593 Tsagarakis George Collin Adam J. Kiprakis Aristides E. 2012 47th International Universities Power Engineering Conference (UPEC) Modelling the electrical loads of UK residential energy users 2014 IEEE Power & Energy Society Innovative Smart Grid Technologies Conference (ISGT) 02 2014 10.1109/isgt.2014.6816509 von Meier Alexandra Culler David McEachern Alex Arghandeh Reza ISGT 2014 Micro-synchrophasors for distribution systems Massachusetts Institute of Technology 1999 Norford L. K. Leeb S. B. Luo D. Shaw S. R. Advanced Electrical Load Monitoring: A Wealth of Information at Low Cost 3 08 2872-2881 28 2013 10.1109/tpwrs.2012.2234142 Miranian Arash Rouzbehi Kumars IEEE Transactions on Power Systems Nonlinear Power System Load Identification Using Local Model Networks 3 05 1530-1536 7 2016 10.1109/tsg.2015.2449904 Rouhani Alireza Abur Ali IEEE Transactions on Smart Grid Real-Time Dynamic Parameter Estimation for an Exponential Dynamic Load Model November 2009 Djokic Sasa Cresswell C.E Collin Adam 2009 IES Annual Conference The Future of Residential Lighting: Shift from Incandescent to CFL to LED light sources 2 05 663-672 21 2006 10.1109/tpwrs.2006.873130 Renmu H. Jin M. Hill D.J. IEEE Transactions on Power Systems Composite Load Modeling via Measurement Approach 8 08 2869-2875 PAS-101 1982 10.1109/tpas.1982.317612 Ribeiro J. Lange F. IEEE Transactions on Power Apparatus and Systems A New Aggregation Method for Determining Composite Load Characteristics Brasil 21 May 2000 Taylor Carson W. Venkatasubramanian Mani V. Chen Yonghong VII Symposium of Specialists In Electric Operational and Expansion Planning Wide-Area Stability and Voltage Control 2017 IEEE PES Innovative Smart Grid Technologies Conference Europe (ISGT-Europe) 09 2017 10.1109/isgteurope.2017.8260251 Kontis Elefherios O. Papagiannis Grigoris K. Syed Mazheruddin H. Guillo-Sansano Efren Burt Graeme M. Papadopoulos Theofilos A. Chrysochos Andreas I. 2017 IEEE PES Innovative Smart Grid Technologies Conference Europe (ISGT-Europe) Development of measurement-based load models for the dynamic simulation of distribution grids August Wiley 1994 978-0-471-94213-9 Pavella M. Murthy P. G. Transient Stability of Power Systems: Theory and Practice 2 05 811-819 26 2011 10.1109/tpwrs.2010.2062542 Mousavi Seyed Mohammad Abyaneh Hossein Askarian IEEE Transactions on Power Systems Effect of Load Models on Probabilistic Characterization of Aggregated Load Patterns 2 03 1661-1662 31 2016 10.1109/tpwrs.2015.2412695 Vignesh V. Chakrabarti Saikat Srivastava Suresh Chandra IEEE Transactions on Power Systems Load Modeling Under Unbalanced Disturbances January 2007 Vanfretti L. Chow Joe H. Aliyu Usman 7th International Conference on Power System Operations and Planning (ICPSOP) Building a Frequency Monitoring Network to Study Dynamics of Rapidly Growing Power Systems 2 04 553-560 30 2015 10.1109/tpwrd.2014.2301219 Regulski P. Vilchis-Rodriguez D. S. Djurovic S. Terzija V. IEEE Transactions on Power Delivery Estimation of Composite Load Model Parameters Using an Improved Particle Swarm Optimization Method Energy Society General Meeting 07 2008 10.1109/pes.2008.4596557 Kosterev Dmitry Meklin Anatoliy Undrill John Lesieutre Bernard Price William Chassin David Bravo Richard Yang Steve 2008 IEEE Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century Load modeling in power system studies: WECC progress update 19 2nd May CRC Press 2014 9781466598652 Short Thomas Allen Electric Power Distribution Handbook 4 12 598-605 2 2011 10.1109/tsg.2011.2162083 Elkhatib Mohamed E. El-Shatshat Ramadan Salama Magdy M. A. IEEE Transactions on Smart Grid Novel Coordinated Voltage Control for Smart Distribution Networks With DG 6 06 1074-1082 99 2011 10.1109/jproc.2011.2114630 Lasseter Robert H. Proceedings of the IEEE Smart Distribution: Coupled Microgrids January New York McGraw-Hill 7 1994 Kundur Prabha Balu Neal J. Lauby Mark G. Power System Stability and Control 1 01 111-120 29 2014 10.1109/tpwrs.2013.2279759 Visconti Igor F. Lima Delberis A. Costa Janaina Mirses C. de Sousa Sobrinho Nobyle Rabello de B. C. IEEE Transactions on Power Systems Measurement-Based Load Modeling Using Transfer Functions for Dynamic Simulations 2013 García Luis Fernando Rodríguez Londoño Sandra Milena Pérez Flórez Juan José Mora Simposio Internacional sobre la Calidad de la Energía Eléctrica - SICEL Dynamic load modeling for small disturbances using measurement-based parameter estimation method 2017 IEEE Power & Energy Society General Meeting (PESGM) 07 2017 10.1109/pesgm.2017.8273973 Zhang Kaiqing Zhu Hao Guo Siming 2017 IEEE Power & Energy Society General Meeting Dependency analysis and improved parameter estimation for dynamic composite load modeling October International Centre for Energy, Environment & Development 2012 Eleri Ewah Otu Ugwu Okechukwu Onuvae Precious Expanding access to pro-poor energy services in Nigeria 9 06 1213-1221 33 2005 10.1016/j.enpol.2003.11.018 Ikeme J. Ebohon Obas John Energy Policy Nigeria's electric power sector reform: what should form the key objectives? 10 66-72 163 2018 10.1016/j.epsr.2018.05.026 Lv Jiaqing Pawlak Mirosław Annakkage U.D. Bagen Bagen Electric Power Systems Research Statistical testing for load models using measured data 1 157-166 9 1994 10.1109/59.317546 Karlsson D. Hill D.J. IEEE Transactions on Power Systems Modelling and identification of nonlinear dynamic loads in power systems New York McGraw-Hill 1994 Taylor Carson W. Maratukulam Dominic Balu Neal J. Power system voltage stability 2015 IEEE PES Asia-Pacific Power and Energy Engineering Conference (APPEEC) 11 2015 10.1109/appeec.2015.7381020 Hua K. Q. Vahidnia A. Mishra Y. Ledwich G. 2015 IEEE PES Asia-Pacific Power and Energy Engineering Conference (APPEEC) PMU measurement based dynamic load modeling using SVC devices in online enviroment 2017 IEEE Power & Energy Society General Meeting (PESGM) 07 2017 10.1109/pesgm.2017.8273913 Wang Xiaozhe 2017 IEEE Power & Energy Society General Meeting Estimating dynamic load parameters from ambient PMU measurements 02 230-239 167 2019 10.1016/j.epsr.2018.10.036 Saviozzi M. Massucco S. Silvestro F. Electric Power Systems Research Implementation of advanced functionalities for Distribution Management Systems: Load forecasting and modeling through Artificial Neural Networks ensembles 6 681 151 2004 10.1049/ip-gtd:20041070 Azmy A.M. Erlich I. Sowa P. IEE Proceedings - Generation, Transmission and Distribution Artificial neural network-based dynamic equivalents for distribution systems containing active sources Glasgow, Scotland, UK July 2008 Wenzel T. Leibfried T. Retzmann D. 16th Power Systems Computation Conference Dynamical simulation of a Vacuum Switch with PSCAD 74 4 81 September 2 2012 Bhavsar Hetal Ganatra Amit International Journal of Soft Computing and Engineering A Comparative Study of Training Algorithms for Supervised Machine Learning Singapore April 2006 doi.org/10.1007/11731139_1 Hand David J. Pacific-Asia Conference on Knowledge Discovery and Data Mining Protection or Privacy? Data Mining and Personal Data 1 01 121-131 29 2014 10.1109/tpwrs.2013.2279263 Gill Simon Kockar Ivana Ault Graham W. IEEE Transactions on Power Systems Dynamic Optimal Power Flow for Active Distribution Networks 2012 You Yi Liu Dong Yu Wenpeng Chen Fei Pan Fei Automation of Electric Power Systems Technology and Its Trends of Active Distribution Network