Modeling and Simulation of Power Consumption at Nonlinear Loads2

Modelling And Simulation Of Power Consumption At Nonlinear Loads

Dejan Stevanović, Predrag Petković and Borisav Jovanović

Laboratory for Electronic Design Automation, Faculty of Electronic Engineering, University of Niš, Aleksandra Medvedeva 14., 18000 Nis, Serbia, phone: +381 18529321, email:

[email protected]

Abstract: Nonlinear loads introduce harmonic distortion into power grid. This produces losses and jeopardises other consumers in the grid. Therefore it is very important to be able to simulate effects of nonlinear loads and afterwards to develop method for their detection and measurement. This paper describes RTL (Register Transfer Logic) model of effective and low-cost distortion power meter. The model is verified with simulation. It was implemented in Matlab and VHDL language. Thereafter it was used for synthesis as a module in an ASIC integrated power meter.

Keywords: power distortion, harmonics, modelling, benchmark

1. Introduction

Generally all loads of a power grid can be classified in two groups: linear and nonlinear. Linear loads characterize currents that track waveform of voltage resulting in sinusoidal with frequency of 50 Hz, or 60 Hz. Until recently, almost all loads were linear: electric motors, light bulbs, different heaters and most of the household appliances. Nonlinear loads drive current characterized with waveforms that differs from sinusoidal voltage [1]. In the last 50 years the number of such loads rapidly increases.

The nonlinear loads can be divided in two groups. The first group comprises equipment used in offices, that is, computers, faxes and most of the appliances with modern electronic control system units. The second group includes different DC motors with adjustable speed drivers. These motors are mostly used in industry, in production processes, and in the elevators. Typical current waveforms for computer and DC motor with adjustable speed, are illustrated in Fig. 1.a and Fig. 1.b, respectively.

(a) (b)Figure 1. Power supply current waveforms for (a) computer,

(b) dc motor

Current waveforms illustrated in Fig. 1 can be obtained by superimposing several sinusoidal waveforms of different frequencies. If one wants to obtain current waveform represented in Fig. 1a, he has to add three sine-waves with frequencies 50Hz, 150Hz, and 250Hz. Waveform in Fig. 1b is result of adding three sine signals with frequencies 50Hz,

250Hz, and 350Hz. Frequency of 50Hz is fundamental frequency, while all other frequencies are frequencies of higher harmonics, representing integer multiple of fundamental frequency. Amplitude and frequency of higher harmonics are dependent on the type of nonlinear load. This helps in identification of particular load type [1].

Unfortunately, distorted current flows-back to the power grid and introduces additional high-frequency voltage drop [1]. This “pollutes” purity of sine-wave voltage that supplies all loads connected to the power grid. Due to the final values of impedances on power line, all nearby loads are more affected. Fig. 2 shows impact of distorting load on the neighbour loads. The distortion is smallest in point 1 and the largest point 3 because the line impedance rises with the distance between load and the substation.

Figure 2. Impact of nonlinear load.

As one can conclude from Fig. 2, the distortion is a phenomenon where all loads connected to a power grid mutually interfere to each other. Therefore the increased number of nonlinear loads raises power of harmonic distortion of the complete system. So they affect both the components of the distribution system and all other loads. It is important to maintain the distortion of the voltage within acceptable limit. Therefore it is necessary to measure the distortion, and then apply all appropriate measures for its reduction.

The paper is organized in seven parts. The next section describes influence of harmonic distortions on other electrical units connected to the grid. The third section explains how to calculate power of nonlinear loads in monophase power system. The subsequent section defines discrete-time models for power consumption calculation. The fifth part describes models for segments of power grid. Results of simulations that verify proposed models are presented in the sixth section. The last section articulates conclusions.

2. Importance of distortion power detection for power grid

The previous section enlightened how nonlinear loads introduce nonlinear distortion into the power system. It is important to recognize what threats they represent for other power consumers and for the power distribution equipment. Therefore this section will briefly analyse the impact of line voltage distortion for these two categories of power system components.

Electrical equipment reacts differently to harmonic distortions of power supply depending on the function it performs. For example distorted voltage has no effect to light bulbs. On the other hand there is a large group of equipment that relay operating function on sine-wave voltage supply. Their best representatives are induction motors. Any deformation in voltage waveform introduces loss in form of increased coil temperature causing rapid destruction of isolation. Undoubtedly this reduces the life of motor [1].

Besides, some equipments require very precise supply voltage. Harmonic distortion may cause a malfunction of the devices. This category comprises all devices that utilize thyristor based control such as dimmers or some soldering tools are.

Harmonic distortions negatively affect power system. For example the neutral line current in a three-phase power system may exceed the value of active power line. In single phase system the harmonic distortions raises a risk of overloading the neutral line. This usually causes:

Overheating of neutral line, with reducing the life span of the conductor and with possibility to cause fire.

High voltage between neutral line and ground can affect the operation of digital equipment and local area network (LAN), if the grounding is bad [2].

The distortion current causes additional heating of transformer and therefore reduces their lifespan. On the other hand, when distortion voltages are present in supply voltage for capacitor batteries, dielectric is overheating and threats to explode.

All this justifies the effort to avoid and/or diminish the amount of power distortion. One of important steps in that direction is to understand the physical nature of the phenomenon in order to make good simulation models. Thereafter it will be possible to recognize procedures that will help to detect the source of pollution and to measure its value.

The following section gives definitions that will help to establish a procedure for distortion power modelling, simulation and measurement.

3. Distortion power modelling in nonlinear monophase power systems

Calculating the power of nonlinear loads is more complex compared to the case when current is sine function. The instantaneous values for voltage and current containing M

harmonic components will be given by the following equations:

(1)

(2)

where Vh and Ih are the amplitudes of the hth harmonic of the voltage and current, respectively. RMS values for voltage and current expressed by formulas (1), (2) are defined as:

(3)

(4)

where VRMSh, i IRMSh are the RMS values of the hth harmonic of the voltage and current, respectively.

Product of the voltage and current on the same harmonic frequency gives the harmonic power. For mono-phase systems total active power is given by:

(5)

Reactive power is defined as:

(6)

The contribution of harmonic components of voltages and currents to the total active and reactive power is small. Typically less than 3% of the total active and reactive power [3]. The main contribution of harmonic components of voltages and currents is related to the distortion power. Vector sum of active and reactive power gives the phasor power [3] S. Its intensity is defined as:

, (7)

where active power P is the algebraic sum of the active power for the fundamental harmonic and active powers of all harmonics (5), and Q represents the algebraic sum of the reactive power for the fundamental harmonic and reactive powers of all harmonics (6).

On the other hand, apparent power U represents vector sum of phase and distortion power [3], so that its intensity is calculated as:

. (8)

Term distortion power D, which is an integral part of the apparent power, was introduced by C. Budeon in 1927 [4].

Fig. 3 illustrates geometrical relationship between active P, reactive Q, phasor S, distortion D and apparent power U, when currents and voltages have higher harmonics for single-phase system.

Figure 3. Geometrical relationship between active, reactive, phasor, distortion and apparent power.

According to Fig. 3 it is obvious that distortion power will be equal to zero and apparent power U will be equal to phasor power S if there is no distortion (no nonlinear load).

4. Discrete-time models for power consumption

Today all power-meters relay on digital signal processing of samples of instantaneous voltage and current values. Therefore the practical application requires discrete-time models of all power components. The front-end of electronic power meters are analogue to digital converters that convert analogue values of voltage and current samples (taken in equidistant time intervals) into digital values. Instantaneous value of current as function of time can be represented in the form:

(9)

After the discretization in time, it becomes:

(10)

where f = 50Hz, fsempl = 4096Hz, are frequency of the power grid voltage and sampling frequency, respectably. RMS value of the current is calculated in the circuit according to the formula:

(11)

where N=4096. Similar expression is used when calculating RMS value for the voltage.

Instantaneous value of power is obtained by multiplication of instantaneous values of current and voltage. Hence, average active power one gets in form:

(12)

The same model is used for reactive power after voltage and curent samples are shifted for /2. Possible sources of error in active and reactive power calculation using this model are caused with the phase difference between voltage and current values and the fact that power-network frequency is slightly changed around the nominal (50Hz). In order to eliminate errors, after the multiplication of the current and voltage values, the values i2(t), u2(t), p(t) and q(t) are filtered and accumulated. With known P and Q one can calculate apparent power according to

, (13)

that is only other interpretation of (8) [3].Now, according to (8) one easily can compute distortion

power as:

(14)

Previous equations represent bases for RTL model development. Accordingly, model for DSP module capable to calculate all powers and energies required by power providers and consumers involved in public power grid has been developed.

Firstly it was implemented in Matlab and thereafter in VHDL to provide possibility to be implemented in hardware. Simple numerical integration of P, Q, U, D and S in time gives appropriate energies.

The model provides four-quadrant measurements as Fig. 4 indicates.

The model is based on multiply implementation of block diagram consisting of multiplier, Low-pass filter (LPF) accumulator and square-root block as presented in Fig. 5. Practically IRMS and VRMS models have the same architecture when i(nT) or v(nT) are supplied to input. Model for P differs only in feeding multiplier with both i(nT) and v(nT).

Model for Q has identical structure but it is fed with voltage samples displaced for /2.

Apparent power samples are calculated directly applying (13).

Figure 4. Four-quadrant representation of delivered and consumed power

(a)

(b)

Figure 5. Block diagram of model for IRMS and VRMS

calculation

These models were confirmed by simulation. Moreover they have been verified on prototyped solid-state power meter realised as ASIC [5, 6].

Therefore this paper focuses to approve model for distortion power calculation. Actually, the model can be derived from the previous. Figure 6 represents its architecture and it operates as follows.

Figure 6. Block diagram of circuit for calculating the distortion power

The multiplier accepts samples of apparent power U trough Data port. After 24 clock cycles required for 24-bit

signal using Booth’s algorithm the squared value of the apparent power U2 appears and being stored. Thereafter value of the active power is squared and the new value is subtracted from the value of apparent power. The same process is repeated for reactive power Q. Finally, the obtained value is sent to the input of the square root block that provides distortion power D. FSM block provides control signals that schedule correct operation.

5. Modelling of power line network

In order to simulate impact of nonlinear distortion to power grid one needs not only the proper model for “measurement” equipment but requires models for loads, as well. There are several programs that allow using on-shelf simulation models. One of the most popular programs for simulation and modelling is Simulink package that is an integral part of Matlab interactive environment that enables computationally intensive tasks.

The power grid is modelled as a power transmission line with all substations.

As an example Fig. 7 illustrates part of a power grid that decreases the voltage from 10kV to 230V, which is used to power single-phase device.

Figure 7. Simulink model of loads and transmission lines

Power line losses are modelled with section as Fig. 8 presents.

Figure 8. section

Linear loads in the power grid can be modelled in two ways:

a) as a serial connection of inductance and resistance,b) as a parallel connection of inductance and

resistance.Serial connection of inductance and resistance is used to

represent a particular linear load. However if one wants to represent a group of linear loads, the parallel connection is more appropriate [7].

6. Results of simulations

All developed models are verified by several simulations. We have simulated power network loaded with:

a) Heaterb) Induction motorc) 6-pulse three phase diode rectifier dc power supply

d) 6-pulse switched-mode power supply.

All of them were supplied with sine-wave voltage slightly distorted with allowed 5% THD. Actually it corresponds to the sine characterized with 50Hz and 220V RMS but with flattened top values.

The first two cases represent linear loads. Therefore the obtained currents track the voltage waveform.

Cases denoted above with c) and d) represent nonlinear loads. Consequently they draw distorted current. In order to approve model for distortion power calculation we use the measured data for currents published in [7]. As already known to power electronic community, the data are suitable be used as benchmark. Fig. 9.a gives graphical interpretation of current through 6-pulse three phase diode rectifier dc power supply while Fig. 9.b shows current waveform trough 6-pulse switched-mode power supply.

a)

b)Figure 9. Current waveforms for a) 6-pulse three phase

diode rectifier dc power supply, b) 6-pulse switched-mode power supply

Table 1. summarizes the results obtained by simulation with model presented in Fig. 5 and Fig. 6.

Table 1 –Simulation results for power consumption of different types of loads

a) b) c) d)

IRMS (A) 7.08 7.08 9.8 10.5

URMS (V) 230.3 230.29 230.29 230.29

P (W) 1630.4 1411.7 1657.3 1544.2

Q (VAR)K

0 815.77 391.23 291.56

S (VA) 1630.4 1630.45 1702.85 1571.48

U (VA) 1630.4 1630.4 2258.5 2416.1

D (VAR) 0 0 1483.5 1835.2

As expected, resistive load, the heater, resulted with only with active power as column a in Table 1 shows. Therefore P equals to phasor power S and to apparent power U. Induction motor is example of another linear load. Results of simulation are listed in column b. It is obvious that it

introduces significant reactive component but null distortion power was registered.

Apart from linear loads the nonlinear load of 6-pulse three phase diode rectifier dc power supply introduced remarkable distortion power together with reactive component as column c in Table 1 shows. One easily observes that the waveform presented in Fig. 9.b has greater distortion than the previous one. Therefore it is expectable that distortion power in case of 6-pulse switched-mode power supply be greater. Result for simulated distortion power presented in the bottom row of column d in Table 1 proves this expectation.

Now, with the summarized results it is obvious that nonlinear loads cause significant losses to power providers. Actually almost all electronic power meters are able to register only phasor power S. In cases of two nonlinear loads denoted as c and d, the losses reach even 32.63% and 53.75% respectively. Even if apparent parent is measured it is important to detect consumers that introduce harmonic pollution into the power grid. This is possible only with measuring the amount of harmonic pollution. We suggest the solution for distortion power measurement presented in Fig. 6 as effective and not expensive. Armed with information about the value of distortion, power providers are able to detect and penalize consumers that enter harmonic distortion into the power grid.

7. Conclusion

This paper addressed to a very significant issue of modelling and simulation of power consumption in presence of nonlinear loads. The importance rises with increased number of electronic equipment that introduces harmonic distortion into the power grid. We considered models for metering active, reactive, phasor, distortion and apparent power. Contemporary power meters relay on mixed signal system on chip that converts analogue samples of line voltage and current to discrete-time digital signals. Thereafter measurement is transformed to digital signal processing. The tricky part is to find smart algorithm that provides needed accuracy. Therefore it is reasonable and practical to generate model at RTL level that will be suitable for hardware synthesis. With that goal we developed model for distortion power metering. The model has been verified on several examples of different types of loads. It was coded in Matlab and VHDL. Afterwards we utilized VHDL code for hardware synthesis using Cadence design tool and AMIS 035 CMOS technology. The proposed RTL model has become part of DSP block in a solid-state power meter. The enlargement of DSP related to distortion power metering occupies only 569µm x 564µm of the chip area.

ACKNOWLEDGE

Results described in this paper are obtained within the project TR32004 founded by Serbian Ministry of Science and Technology Development.

REFERENCES

[1] “Harmonic Distortion in the Electric Supply System” Integral Energy Power Quality Centre: Technical note No. 3, March 2000

[2] T. Shaughnessy, “Clearing Up Neutral-to-Ground Voltage Confusion”, Electrical Construction & Maintenance, February 1, 2007.

[3] J. G. Webster, “The measurement, instrumentation, and sensors handbook”, IEEE Press, 1999.

[4] A. E. Emanuel, “Summary of IEEE Standard 1459: Definitions for the Measurement of Electric Power Quantities Under Sinusoidal, Nonsinusoidal, Balanced, or Unbalanced Conditions”, IEEE Tran. On Industrial Applications, Vol. 40, No3, May 2004.

[5] B. Jovanovic, M. Damnjanović, P. Petković, “Digital Signal Processing for an Integrated Power Meter”, Proceedings of 49. Internationales Wissenschaftliches Kolloquium, Technische Universirtat Ilmenau, Ilmenau, Germany, vol. 2, pp. 190-195, September 2004

[6] B. Jovanović, M. Damnjanović, “Digital Signal Processing in three-phase Integrated Power Meter”,

Proc. of the 52nd ETRAN conference, Palić, June 2008, EL2.3-1-4.

[7] George J. Wakileh, “Power Systems Harmonics”, Springer, 2001

Author Biographies

Dejan Stevanović was born in Vranje, Serbia in 1982. He received the Dipl.-Ing. (M.S.) degree from the University of Niš, in 2007. He is student of third years of PhD studies at Faculty of Electronic Engineering and has been member of Leda laboratory since 2007. His current research interests are power quality and digital integrated circuits design.

Predrag Petković was born in Čačak, Serbia. He received Ph.D. degree from the University of Niš, in 1990. He is currently full professor at University of Niš, Faculty of Electronic Engineering. His research interests include ASIC design, optimisation, modelling, and simulation focusing on symbolic circuit simulation, power quality and mixed signal integrated circuits design.

Borisav Jovanović was born in Niš, Serbia in 1979. He received the Dipl.-Ing.(M.S.) degree from the University of Niš, in 2002 and he is currently teaching assistant at the Faculty of Electronic Engineering, University of Niš. His research interests include computer aided design of electronic circuits, electronic circuit simulation, ASIC design.