Analytical and experimental discussion of a circuit-based model for compact fluorescent lamps in a 60 Hz power grid

This article presents an analysis and discussion on the performance of a circuit-based model for Compact Fluorescent Lamps (CFL) in a 120 V 60 Hz power grid. This model is proposed and validated in previous scientific literature for CFLs in 230 V 50 Hz systems. Nevertheless, the derivation of this model is not straightforward to follow and its performance in 120 V 60 Hz systems is a matter of research work. In this paper, the analytical derivation of this CFL model is presented in detail and its performance is discussed when predicting the current of a CFL designed to operate in a 120 V 60 Hz electrical system. The derived model is separately implemented in both MATLAB® and ATP-EMTP® software using two different sets of parameters previously proposed for 230 V 50 Hz CFLs. These simulation results are compared against laboratory measurements using a programmable AC voltage source. The measurements and simulations considered seven CFLs 110/127 V 60 Hz with different power ratings supplied by a sinusoidal (not distorted) voltage source. The simulations under these conditions do not properly predict the current measurements and therefore the set of parameters and/or the model itself need to be adjusted for 120 V 60 Hz power grids.


Introduction
The constant increase of non-linear loads in low voltage grids, specifically the mass adoption of Compact Fluorescent Lamps (CFLs) and Light-Emitting Diode (LED) based lamps, aimed at reducing power demand and improving energy efficiency in lighting systems, has led to high levels of harmonic content in the current drawn from the supply system (Blanco & Parra, 2011) (Romero, Zini, & Ratta, 2011) (Ribeiro, et al., 2011).Therefore, the search for more and better models to assess and predict the collective harmonic impact of these loads on the low voltage network is currently a research topic (Salles, Jiang, Xu, Freitas, & Mazin, Oct. 2012).Moreover, several serious problems are caused by the harmonic currents flowing in the power system: overheating and overloading of conductors (especially neutrals), motors and transformers (increased losses); poor power factor and overloaded capacitor banks; undesired protection tripping and skin effect in conductors (Malagon-Carvajal, Ordonez-Plata, Giraldo-Picon, & Chacon-Velasco, 2014), among others.Considering these facts, there is an urgent need for better models that allow assessing, on the short and medium time scales, the potential impact of nonlinear lighting loads in 120 V 60 Hz low voltage distribution networks.The first section of this paper presents some scientific literature related with diversity and attenuation, as well as a review of nonlinear loads models.The next section describes each of the parameters involved in the CFL circuit-based model.The model was originally developed for 230 V 50 Hz electrical systems and in this paper there is a discussion on whether it performs well for 120 V 60 Hz grids.Then, in the study case, the current estimated by the circuit-based model is compared with measurements from CFLs with sinusoidal voltage supply and different rated powers.

Preliminaries and Previous Work
The CFL loads induce highly distorted currents due to the use of power electronics in their operation.However, despite the current drawn by a single CFL is quite low, a large number of customers using a few of these loads per household could cause significant power quality problems (Matvoz & Maksic, 2008) (Blanco, Stiegler, & Meyer, 2013).The impact of these problems can be assessed if the attenuation and diversity phenomena are correctly estimated by accurate models.Attenuation is defined in (Mansoor, et al., 1995) and (Mansoor, Grady, Chowdhury, & Samotyi, 1995) as the interaction between the distorted voltage and current, mainly due to the common system impedance.As a result of this interaction, when the source voltage is distorted, a reduction in current harmonics produced by other loads can take place (Salles, Jiang, Xu, Freitas, & Mazin, Oct. 2012).
On the other hand, the phenomenon of diversity is defined as the partial cancellation of harmonic currents in different lighting loads at the common coupling point.This cancellation is due to the dispersion in the phase angles of the currents, which is related to the structural characteristics of the load and variations in either the demand or parameters such as the rated power and power factor (Mansoor, et al., 1995) (Mansoor, Grady, Chowdhury, & Samotyi, 1995) (Task Force on Harmonics Modeling and Simulation, 1996).
Research in the area of CFLs is aimed at assessing the phenomena described above.Some studies consider experiments in the laboratory (Blanco, Stiegler, & Meyer, 2013) (Rawa, Thomas, & Sumner, 2012).Others consider measurements and simulations (Djokic & Collin, 2014), and some consider only simulations (Nassif & Acharya, 2008), but still without conclusive results.
In the same vein, this paper focuses on a novel analytical model of CFLs developed through several measurements in a 230 V 50 Hz grid and implemented via script programming (Cresswell, 2009), (Collin A. J., 2013).The aim of this paper is to implement this model on simulation platforms (MATLAB ® and ATP-EMTP ® ), so as to allow changes on the parameters and thus verify its performance in 120 V 60 Hz systems.

The Circuit-based CFL Model
The CFL circuit model is developed and described in detail in (Cresswell, 2009) and (Collin A. J., 2013).A discussion about the accuracy of this model at 50 Hz frequency with Sinusoidal Voltage supply is presented in (Collin, Djokic, Cresswell, Blanco, & Meyer, June 2014).
The model consists of (See Figure 1): a rectifier bridge, an input resistance (R CFL ), an input filter (L CFL or X L_CFL ), a dc link capacitance (C DC ), and an equivalent resistance (R EQ ) which is a function of the instantaneous dc link voltage (V DC ).
The circuit model is implemented in ATP-EMTP ® allowing a comprehensive analysis of the CFL under sinusoidal and nonsinusoidal supplying voltage conditions.However, the trigger times for charge and discharges stages are previously calculated in MATLAB ® through a script program.The model on these platforms enables different changes on the parameters and facilitates the study of their impact on simulation results.

Analytical CFL model derivation
The CFL model derivation is based on the information presented in (Cresswell, 2009) and (Collin A. J., 2013).However, the CFL model script provided by (Cresswell, 2009) does not specify the solution method for the differential equation system, so that their implementation is not completely reproducible.On the other hand, (Collin A. J., 2013) proposes a generic model for a Switch Mode Power Supply (SMPS), and, unlike (Cresswell, 2009), specifies the trapezoidal integration method used to solve the differential equation system.Moreover, (Collin A. J., 2013) presents the derivation of equations for the instantaneous input current (I in ) and the instantaneous dc link voltage value (V DC ) in the SMPS model.Nonetheless, some typos make it difficult to follow those derivations.
In this paper, the analytical CFL model derivation is presented including the analysis of the charging and discharging stages (See Figure 1).These expressions are then used for the implementation of the models in MATLAB ® and ATP-EMTP ® .The derivation starts from the KVL for each stage: Charge Stage Rewriting the differential equations system (Equation (1) and Equation ( 2)) and neglecting (R IN , L IN ): From Equation (1): From Equation ( 2): The matrix form of Equation ( 5) and Equation ( 7) is: Where: From Equation ( 8): Applying trapezoidal integration method on Equation (13): From Equation ( 13): (16) The matrix form of Equation ( 19): Where: From Equation (21): ( ) Where: Solving the system in Equation ( 23): Instantaneous input current: Instantaneous dc link voltage:

Equivalent Resistance (R EQ )
The high frequency inverter and compact fluorescent tube are represented by the equivalent resistance.This equivalence results from multiple measurements of the instantaneous voltage and current at the CFL dc link in steady state.
The measurements exhibit a change when the magnitude of supply voltage varies (Collin A. J., 2013).Two regions are clearly defined and connected by two transition stages for the rectifier circuit: charge stage and discharge stage.
The capacitor discharge stage is the region of the upper limit and it can be described by an approximately linear function.The region of the lower limit is the capacitor C DC charging stage.However, in this it may be observed that the relationship between the equivalent resistance and V DC has a strong arc geometry.
In this is two analytic functions: linear polynomial function the and a for ).

Input filter (L CFL − X L_CFL )
The inductance L CFL represents an input filter which induces an oscillation at the peak of the input current waveform.It may or may not be included in the CFL model depending on the specific components used in the ballast circuit.The inductance value is small and has little impact on loworder harmonics due to the large resistance and capacitive reactance of the conduction path.From measurements, a specific per-unit value of X L_CFL is usually adopted according to (Collin, Djokic, Cresswell, Blanco, & Meyer, June 2014).
That value is used in this work.

DC link capacitance (C DC )
The C DC value is defined as a trade-off between two considerations: complying a standard harmonic distortion limit, e.g.(IEC 61000-3-2 ed4.0, 2014), and satisfying a specified tube life time.Multiple measurements show that the size of dc link capacitance is directly related to the CFL rated power.This can be compared against several manufacturers' specifications and available design data (Collin A. J., 2013).
For compact fluorescent lamps with rated power of 5 W to 25 W, typical values of C DC are between 1 µF to 5 µF (Ranging from 0.2 µF ).In this way, C DC is defined as a linear function of CFL rated power resulting in a relation for dc link capacitance given by the following expression (Collin A. J., 2013): Where f is the frequency and X C DC is the capacitive reactance.

Study Case
In this study case, the performance of circuit-based sinusoidal voltage source is 120 V (60 Hz).The laboratory measurements for seven CFL 110/127 V with different power ratings are compared with simulated MATLAB ® and ATP-EMTP ® circuit-based models.
The parameters for different simulations are presented in Table 1.It can be noted that, unlike CFL (or XL CFL ), C DC (or ) and R CFL ; the equivalent resistance (R EQ ) is independent of the CFL power rate.
Initially, an 11 W 230 V 50 Hz CFL is tested using the controlled AC voltage source.This measurement is compared with the simulations of the circuit-based models.
The models satisfactorily predict the current distortion; however, the circuit of the measured lamp can be slightly different than the simulated one.L CFL (X L CFL ) might be smaller or not present in the actual lamp considering the small oscillation at the peak of the measured input current waveform and the slightly difference with the current predicted by the model (See and Figure 2).Nevertheless, this requires further investigation.

Parameters for simulation (R EQ , R CFL , L CFL -X L CFL , -X C DC )
The same experiment is carried out for CFLs with different power ratings (5 W, 11 W, 15 W, 18 W, 20 W, 25 W and 27 W) supplied by a 120 V 60 Hz power grid.As an example, Figure 4 and Figure 6 show the waveforms of simulated and measured current for 20 W and 25 W CFLs, respectively.It can be noted that the simulations identify charging and discharging intervals and partially predict the current waveform during charging stage.Nevertheless, the current magnitude from simulations are way smaller than the measured current in both cases.Further research is needed to correct these drawbacks.* This parameters are taken from (Cresswell, 2009) and (Collin A. J., 2013) And R EQ (R EQ,CH -R EQ, DISCH ) from Equations ( 27)-( 30) for 120 V.
In order to compare the different results of the simulations, some indices are proposed.The Harmonic Order indices HO h for the different signals on the magnitude of the harmonic spectrum (Figure 5 and Figure 7) is evaluated.
This analysis is performed on each harmonic order of current signals for different CFL power rated (Table 2), as shown in the following expression: Mag 1 measure: Harmonic magnitude measure for first harmonic.
Mag h simulation:Harmonic magnitude simulated for each harmonic and for each implemented model.Additionally, the Features (Max Value and Energy) are proposed and presented in Table 3.In Table 2 and Table 3, it can be observed that the larger the CFL power rating, the larger the error in the description of distortion current in the simulated models.
For instance, in the bottom right corner of Table 3, for the 5 W CFL, the Delta Average between Max-feature measure and Max-feature simulation result is 166.82 mA, and the Delta Average between Energy-feature measure and   Additionally, the results of a study case suggest that the different models do not predict the behavior of the distorted current under sinusoidal voltage supply conditions for 120 V 60 Hz systems, even if they have a good performance for a 230 V 50 Hz sinusoidal supply voltage.
For future research, it is important to find the circuit-based model parameters that describe correctly the CFL distorted input current under a 120 V 60 Hz power supply.Likewise, the study of performance of the existing model (230 V 50 Hz) under non-sinusoidal conditions and the effects of diversity and attenuation phenomena on different power quality indices should be studied via simulations and measurements in a low voltage distribution grid.

Figure 2 .
Figure 2. Simulated and measured current for an 11 W 230 V 50 Hz CFL.

Figure 3 .
Figure 3. Spectra of simulated and measured current for a 25 W 120 V 60 Hz CFL.

Figure 4 .
Figure 4. Simulated and measured current for a 20 W 120 V 60 Hz CFL.

Figure 5 .
Figure 5. Spectra of simulated and measured current for a 20 W 120 V 60 Hz CFL.

Figure 7 .
Figure 7. Spectra of simulated and measured current for a 25 W 120 V 60 Hz CFL.

Conclusions
This paper studies the performance in a 120 V 60 Hz power grid of a novel previously proposed CFL circuit-based model (derived for 230 V 50 Hz systems) via simulations and measurements of CFLs with different power ratings under sinusoidal controlled voltage supply.The analytical derivation for the CFL model is presented in detail along with the solution for the associated differential equation system through the trapezoidal integration method.The equations for Instantaneous input current and Instantaneous dc link voltage are re-derived.The circuit-based models are implemented in MATLAB ® and ATP-EMTP ® .The later easily allows changes in model parameters and simulation of the interactions with other non-lineal load models such as: current source model, equivalent Norton model and other Circuit-based models in a power distribution network.

Table 3 .
Features computed from simulated and measured current for CFLs under test.