Advanced Load Models For Voltage Sag Studies In Distribution Networks

1

Advanced Load Models for Voltage Sag Studies in Distribution Networks J.A. Martinez, Member, IEEE, and J. Martin-Arnedo

Abstract—Voltage sag characteristics derived from simulation are influenced by the models chosen for load representation. This aspect can be crucial for calculation of voltage sag indices based on the undelivered energy. Besides, load representation is a difficult task, since an accurate model has to incorporate voltage and frequency dependency, dynamic behavior, and equipment sensitivity. A random calculation of active and reactive power demands can be also required. This paper presents a summary of the work performed by the authors on load modeling for voltage sag studies using an electromagnetic transients program. A very simple test system is used to analyze and compare the behavior of the implemented load models. Index Terms—Load Modeling, Power Distribution, Power Quality, Simulation.

I. INTRODUCTION

L

oad modeling for dynamic performance analysis has been the subject of a significant effort during the last years [1] – [6]. It is recognized that the representation of the load can have an important influence on simulation results, for instance it is a critical issue when evaluating voltage stability. Load modeling can be also important in voltage sag studies since the model chosen to represent the demand can have a strong influence on some sag characteristics. Although not much effort has been dedicated to the representation of the load in voltage sag studies, some interesting works have been performed and some experience is already available [7] – [9]. In fact, load models to be used in voltage sag studies can be very similar to those proposed for transient stability studies, since in both cases slow transients are to be analyzed. The aim of this work is to develop and implement aggregated load models for voltage sag studies in distribution systems using an electromagnetic transients program [10]. The main motivation of the work is the calculation of a voltage sag index based on the undelivered energy in distribution networks [11]. The retained voltage at a node of a radial distribution network is hardly affected by load conditions if the sag is caused by a fault. However, other voltage sag characteristics can be strongly influenced by the approach chosen for representing Juan A. Martinez and Jacinto Martin-Arnedo are with the Departament d’Enginyeria Elèctrica, Universitat Politècnica de Catalunya, 08028 Barcelona, Spain. Jacinto Martin-Arnedo is preparing his Ph.D. with a grant from the Spanish Ministerio de Ciencia y Tecnología.

the load. Important aspects to be considered are listed below. • Field measurements have shown that power demand is voltage dependent, see for instance [12]. • Induction motors constitute a significant percentage of the load in a power system, so the load model has to incorporate a dynamic behavior and a frequency dependency. • The impact of a voltage sag will depend on the percentage of the sensitive equipment that is connected to the system affected by the disturbance; therefore, acceptability curves must be also incorporated into the load model [13]. • If the goal is to predict the characteristic of voltage sags (i.e. density functions of magnitude and duration), the study must be based on a probabilistic approach [14]; therefore the daily variation and the random nature of the load must be also included. Table I shows a summary of load models for voltage sag calculations based on the goal of the study. TABLE I LOAD MODELS FOR VOLTAGE SAG STUDIES GOAL Voltage drop Calculation of voltage sag characteristics

Sag duration Phase jump

Calculation of the undelivered energy

Stochastic pre- Voltage drop diction of voltage sag characte- Sag duration ristics (sags per year) Phase jump Stochastic prediction of the undelivered energy

SOLUTION TECHNIQUE

LOAD MODEL

Steady state/ Time domain It is generally unimportant, a constant impedance reTime domain presentation will suffice Steady state/ Time domain The model has to incorpoTime domain rate voltage dependency, dynamic behavior and sensitivity to voltage sags (acceptability curves) Steady state/ Time domain It is generally unimportant, a constant impedance reTime domain presentation will suffice Steady state/ Time domain The model has to incorpoTime domain rate voltage dependency, dynamic behavior, daily variation (including ran-dom variation) and sensiti-vity to voltage sags (accep-tability curves)

The goal of this work is the development and implementation of different load models for voltage sag studies in distribution networks using the ATP version of the EMTP [15]. The subsequent sections present a summary of models chosen in this work for load representation, the approaches

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followed for ATP implementation of the different models, and a comparison of the behavior of all load models using a very simple distribution test system. The paper is a continuation of a previous paper on the same subject [16]. The present work incorporates new features that are required for a more accurate representation; e.g. sensitivity equipment to voltage sags and random calculation of active and reactive power values. However, there are some important issues related to load modeling that are not covered in this work; for instance, the estimation of load parameters [4], [5], or the effect that load conditions can have on voltage sag characteristics [17].

of such load relies in this work on the Universal Machine module, a built-in capability of the ATP [15]. However, a model has to be also considered for dynamic loads other than induction motors. Fig. 1 shows the diagram of the dynamic load model selected for this work. It is a modified version of a model presented in [5], and is applied to both real and reactive powers with different parameters. V

Np(V)

Gp(s)

+

P +

Pt(V)

II. LOAD MODELING Models for load representation in voltage sag studies have been divided into two main groups: deterministic and probabilistic. In fact, the main difference is the calculation of random numbers that are needed to obtain power initial load values when a probabilistic model is used. A. Deterministic models According to the discussion included in the previous section, a complete load model should include voltage and frequency dependency, dynamic behavior and tolerance to voltage sags. Different models incorporating one or several of these features can be considered. Those developed for this work are detailed below. Since power frequency should not be affected by faults located in the distribution network, this feature has not been incorporated in any model. Only when sags were caused by faults located at the transmission level, a frequency-dependent model should be considered. 1. Static model. A power demand that incorporates voltage dependence can be expressed as follows np

S = P0

∑a V k

+ jQ0

k =0

np

∑a k =0

∑b V

=1

;

np

N p (V ) = P0

k=0

∑b

k

∑a

skV

(2a)

Pt (V ) = P0

∑a

tk V

k

k=0

P = Pr (V ) + Pt (V )

τq

dQr (V ) + Qr (V ) = N q (V ) dt nq

∑b

sk V

k =0

=1

k =0

where P0 and Q0 are respectively the rated real and reactive power at nominal voltage, and V is the p.u. voltage. Equation (1) assumes that there could be a part of a power demand that is voltage-independent. In fact, this is the approach implemented in the majority of load flow programs. By using this approach, the power demand remains the same irrespectively of the values of bus voltages. This is not a realistic model for voltage sag calculation, as it would mean that even for very low retained voltages, the demand will be the same as that prior to the sag. A V1 dependence means that the load behaves as a constant current source, while a V2 dependence means that a load behaves as a constant impedance. 2. Dynamic model. Since a significant percentage of the electric consumption is constituted by induction motors, the load model has to include a dynamic performance. Although some models for representation of induction motors based on a block diagram have been developed [1], the representation

− Pt (V )

np

k

(1)

k

k =0

k

nq

k

Several levels of sophistication have been proposed for the model depicted in the figure; in this work the block G(s) is represented as a first order model. Time-domain equations of this model can be written as follows dPr (V ) τp + Pr (V ) = N p (V ) dt

N q (V ) = Q0

nq

k

Fig. 1. Diagram of a dynamic model for active power.

k

− Qt (V )

(2b)

nq

Qt (V ) = Q0

∑b V

k

tk

k =0

Q = Qr (V ) + Qt (V ) where τp and τq are recovery time constants, Pr(V) and Qr(V) are respectively the active and reactive power recoveries, while Pt(V) and Qt(V) are the active and reactive powers of the dynamic part. Pr(V), Qr(V), Pt(V) and Qt(V) are represented by a polynomial expression such as that shown in equation (1), but coefficients for each power component are different. The model described by the above equations is known as exponential recovery model; since not all dynamic loads can be represented by this model, see for instance [9], other approaches can be needed. 3. Hybrid model. It is the model that results from a combination of any of the above models, to which an induction motor load can be also incorporated. 4. Load tripping. Sensitivity or tolerance of equipment to voltage sags can be represented by acceptability curves, also known as voltage vulnerability curves. The CBEMA (Computer Business Equipment Manufacturers Association) and the

3

5

8

Active Pow er (MW )

ITIC (Information Technology Industry Council) curves are two well known examples. Fig. 2 shows the second one; equipment tripping will be produced if the operating point during the event is outside the area surrounded by the two curves. Since sags and swells can simultaneously occur at the same node both limit curves are of interest.

6

4

2

0

4

0

9

12

15

18

21

24

a) Mean value curve 14

2

12

1 0 0.0001

0.001

0.01

0.1

1

10

100

Time [s]

8 6 4

0 7

A complete model results from the incorporation of voltage tolerance curves into the model selected for representing the load, see Fig. 3. Note that the only difference with respect to the model depicted in Fig. 1 is the percentage of load drop, σp, that can result from a voltage sag. σp

Tolerance Curve

Gp(s)

10

2

Fig. 2. ITIC curve.

Np(V)

Probability (% )

V (pu)

6

Hour

3

V

3

+

(1-σp)

P

+ Pt(V)

Fig. 3. Complete dynamic load model.

B. Probabilistic models The daily demand variation will be based on two curves for the active and reactive power, respectively, and a normal probability density function for each power. Fig. 4 shows the curve of the mean value of the active power and the normal probability density function for a given period. Similar information must be considered for the reactive power. The determination of the real and reactive power at a given node for every period will be therefore based on the random generation of three values: the first one will be the fault instant, which is necessary to obtain the mean value of both active and reactive powers, and two additional random values, which are necessary to obtain the final values of both powers, considering the standard deviation for each one. One of the above deterministic models will be used after the values of active and reactive powers have been determined. This approach can be extremely complex if all parameters to be specified in a deterministic model are assumed variable and random.

7.1

7.2

7.3

7.4

P (MW)

b) Probability density function (from 15 to 18 h) Fig. 4. Daily variation curve of the active power.

III. ATP IMPLEMENTATION There is no built-in model in ATP for representing any of the load models described by equations (1) or (2). Fig. 5 shows the implementation used for a static model. The voltage dependence is modeled by means of a controlled current source whose value is adjusted during the initial steps of the simulation. Therefore, the actual transient simulation can start only after the convergence to the rated values has been achieved. Vi

I

Pi = Pirat ⋅

∑a ⋅ V ⋅∑ b ⋅ V np

k

ik

k= 0

i

Q i = Q irat

nq

k

ik

k =0

Fig. 5. ATP representation of a static load model.

A similar approach has been developed for the dynamic model. As for the incorporation of the tolerance curve, it is straightforward: since either the approach used for the static or the dynamic model requires a voltage measurement, this value is used to decide whether the magnitude and duration of the voltage sag will force a trip or not. Another aspect to be considered is the tolerance of the equipment to phase jump; if this must be incorporated, then a phase jump measurement is also required.

4 1.5 P (MW) 1.0 Power

Other works on load modeling using an electromagnetic transients program has been previously reported, see for instance [18], [19].

0.5 Q (MVAr)

IV. SIMULATION RESULTS This section presents some simulation results derived from the models detailed above. The main goal is to compare the performance of different load models during a voltage sag.

Voltage (pu) - LV Side

0.0 -0.5 1.5 1.0

0.5

0.0 200

400

600 Time (ms)

A. Test System

Voltage (pu) - MV Side

2

Voltage (pu) - LV Side

4 km

HV equivalent : 110 kV, 1500 MVA, X/R = 10 Substation transformer: 110/25 kV, 3 MVA, 8%, Yd Lines : Z1/2 = 0.61 + j0.39, Z0 = 0.76 + j1.56 Ω/km Distribution transformers: 25/0.4 kV, 1 MVA, 6%, Dy

0.5 Q (MVAr)

-0.5 1.5

B C

1.0

0.5 A 0.0 1.5 b

1.0 c

a

0.5

0.0 200

Fig. 6. Diagram of the test system.

400

600 Time (ms)

b) Single-phase-to-ground fault

B. Deterministic load models

Fig. 7. Performance of Model 1.

Ps = P0 (0.8V + 0.2V 2 ) ; Pt = P0 ⋅ 0.2V 2

(4) Qs = Q0 (0.2V + 0.8V 2 ) ; Qt = Q0 ⋅ 01 .V2 being the time constants τp = τq = 0.04 s. The study was performed by simulating a fault at Node 1 (MV side) and measuring the voltage sag characteristics at MV and LV sides of Node 2. Voltage sags caused by singlephase-to-ground and three-phase faults were analyzed. Fig. 7 and 8 show some results. In both figures active and reactive

Power

0.5 Q (MVAr)

Voltage (pu) - LV Side

0.0 -0.5 1.5 1.0

0.5

0.0 200

400

600 Time (ms)

800

1000

800

1000

a) Three-phase fault 1.5 P (MW)

1.0 Power

(3)

Q = Q0 (0.2V + 0.2V + 0.6V ) where V is the per unit rms voltage, being P0 = 0.4 MW, Q0 = 0.3 MVAr. The second part is modeled as an aggregated induction motor load with P0 =366 kW; Q0 =239 kVAr. • Model 2. The demand is represented by a constant impedance model and a dynamic load model, see Fig. 1, being the rated active and reactive powers the same for both models: P0 = 0.4 MW, Q0 = 0.3 MVAr. The constant impedance model is internally represented by a parallel R-L combination. The expressions and parameters of the dynamic load model are as follows 4

P (MW) 1.0

0.5 0.0

Voltage (pu) - MV Side

P = P0 (0.8V + 0.2V 2 )

1.5

Voltage (pu) - LV Side

Two different low voltage load models have been analyzed. In all cases the rated powers are the same at both nodes. Their main characteristics are listed below. • Model 1. Active and reactive powers at both load nodes are split into two parts. The first part is modeled as a static load according to the following expressions 2

1000

P (MW)

1.0

0.0

1

800

1.5

4 km 110/25 kV

1000

a) Three-phase fault

Power

Fig. 6 shows the diagram of the two-feeder test system used for the analysis of different load models. The MV side of the substation transformer is grounded through a zig-zag reactance of 75 Ω per phase.

800

Q (MVAr)

-0.5 1.5

B C

1.0

0.5 A 0.0 1.5 b

1.0

a

0.5

c

0.0 200

400

600 Time (ms)

b) Single-phase-to-ground fault Fig. 8. Performance of Model 2.

5

1.5 Pre-fault P

Power

1.0

Pre-fault Q

P (MW)

0.5

Voltage (pu) - LV Side

0.0

Q (MVAr)

-0.5 1.0

C. Probabilistic load models Power demand is time-variant; therefore the effect of a voltage sag will depend on the instant at which the disturbance is caused. The stochastic nature of the load must be incorporated into models when the calculation of the power delivered to the load is an issue; for instance, for the calculation of an energy-based index [11]. The way in which this performance is added to load models was introduced in Section II.B. A new feature, however, should be considered: the variation of the percentage of the sensitive load. Fig. 10 shows the curves assumed for the present work. Note that power curves depict the mean values, so a density function should be added for each time interval. Since statistical calculations are not performed in this study, this aspect is unimportant. Three cases were simulated in order to illustrate the importance of these modeling features. Simulation results are shown in Fig. 11, they correspond to voltage sags caused by different types of faults that occurred at different hours. All simulations were based on Model 2, described in the previous section. Although computer simulation is not necessary to conclude that results can be very different, these plots prove that the variation of the load can be an important issue for some calculations. However, one must be careful with these conclusions since protective devices were not included in the test system model. Simulations with a more realistic model could provide results and conclusions different from those derived from the present work. The coordination of protective devices and tolerance curves is therefore another important issue. 1.00

Power (MW / MVAr)

power plots correspond to three-phase values, and they were measured at the LV side of the distribution transformer. Although a constant impedance model can be considered as a particular case of voltage-dependent load (it has a V2 depen-dence), it does not behaves as a static load model, since the representation as a parallel R-L has a dynamic performance. The study was completed by incorporating the ITIC curve to the above models and by assuming that 50% of the static load in Model 1 and 50% of the dynamic load in Model 2 were sensitive to voltage sags. Since single-phase-to-ground faults are not too severe, only three-phase faults were simulated. As the ITIC curve can be applied only to singlephase loads, the LV side demand for both models was represented by means of single-phase models, although this aspect is irrelevant since only three-phase faults were simulated. The new simulation results are shown in Fig. 9; they correspond to the same cases that were presented in Fig. 7 and 8 for three-phase faults. The consequences of voltage sags can be easily deduced: post-disturbance values of active and reactive powers are smaller than pre-fault values, while voltage values are larger. In addition, one can observe for an induction motor load that, although the final steady state power values are very different from those obtained without incorporating tolerance curves, the simulation results are very similar during the transients originated at the sag initiation and the voltage recovery. According to the lower ITIC curve, see Fig. 2, the variation of the actual power demand is produced during the fault condition; however, the voltage drop is so severe in all cases shown in the figure that the power delivered is very low and the variation is very small during the fault.

0.40

Reactive

0.20

0

3

6

9

400

600 Time (ms)

800

15

18

21

24

a) Mean active and reactive power values

1000

100

Pre-fault P

Percentage (%)

1.5 1.0

12

Hour

0.0

a) Model 1 Power

0.60

0.00

0.5

200

Pre-fault Q

0.5 0.0

Voltage (pu) - LV Side

Active

0.80

Q (MVAr)

P (MW)

-0.5 1.0

80 Total sensitive load

60 Dynamic sensitive load

40 Static sensitive load

20

0.5

0 0.0 200

0 400

600 Time (ms)

800

1000

3

6

9

12

15

18

Hour

b) Model 2

b) Percentage of sensitive equipment

Fig. 9. Performance of load models incorporating sensitive equipment.

Fig. 10. Power demand at Node 2.

21

24

6

curves. Not much literature has been published on the behavior of three-phase equipment during any type of voltage sag and considering any aspect that can influence the final result, e.g. phase jump.

1.0

Voltage (pu) - LV Side

Power

P (MW) Pre-fault P

Pre-fault Q

Q (MVAr)

0.5

0.0 1.5 b 1.0

VI. REFERENCES a

0.5

c

[1]

0.0 200

400

600 Time (ms)

800

1000

[2]

a) Single-phase-to-ground fault – 0 to 3 h 1.0

Power

Pre-fault P

P (MW)

Pre-fault Q

[3]

0.5

Voltage (pu) - LV Side

Q (MVAr) 0.0 1.5

[4] b

1.0

a

0.5

c

[5]

0.0 200

400

600 Time (ms)

800

1000

[6]

b) Single-phase-to-ground fault – 9 to 12 h [7]

1.0

Power

Pre-fault P

Pre-fault Q P (MW)

0.5

[8]

Voltage (pu) - LV Side

Q (MVAr) 0.0 1.0

[9] 0.5

[10]

0.0 200

400

600 Time (ms)

800

1000

c) Three-phase fault - 15 to 18 h Fig. 11. Probabilistic load model performance.

V. CONCLUSIONS Load representation can be a crucial aspect in voltage sag studies. Depending on the goal of the study, a time-domain solution technique can be needed to obtain a solution of the system response. This paper has presented the implementation of different load models in an EMTP-like tool. Although there was previous experience in this field, the models developed for the present work incorporate some new features, e.g. random nature, equipment sensitivity. It is evident from simulation results that a representation of the load must be carefully made for an accurate calculation of some voltage sag characteristics, e.g. calculation of the voltage profile or lost energy during the sag. Another important conclusion is that most factors to be specified in a load model (factors for voltage dependency, time constants, acceptability curves) can have a strong influence on the simulated results. Finally, a probabilistic approach is advisable if the prediction of voltage sags is to be based on a Monte Carlo solution [14]. An important drawback for the development of a very accurate load model is the limited knowledge of tolerance

[11] [12] [13] [14]

[15] [16] [17]

[18]

[19]

IEEE Task Force on Load Representation for Dynamic Performance, “Load representation for dynamic performance analysis,” IEEE Trans. on Power Systems, vol. 8, no. 2, pp. 472-482, May 1993. IEEE Task Force on Load Representation for Dynamic Performance, “Bibliography on load models for power flow and dynamic performance simulation,” IEEE Trans. on Power Systems, vol. 10, no. 1, pp. 523-538, February 1995. IEEE Task Force on Load Representation for Dynamic Performance, “Standard load models for power flow and dynamic performance simulation,” IEEE Trans. on Power Systems, vol. 10, no. 3, pp. 13021313, August 1995. Ch. J. Lin et al., “Dynamic load models in power systems using the measurement approach,” IEEE Trans. on Power Systems, vol. 8, no. 1, pp. 309-315, February 1993. D. Karlsson and D.J. Hill, “Modelling and identification of nonlinear dynamic loads in power systems,” IEEE Trans. on Power Systems, vol. 9, no. 1, pp. 157-166, February 1994. K. Morison, H. Hamadani and L. Wang, “Practical issues in load modelling for voltage stability studies,” IEEE PES General Meeting, July 2003, Toronto. S. Ihara, K. Tomiyama and M. Tani, “Residential load characteristics observed at KEPCO power system,” IEEE Trans. on Power Systems, vol. 9, no. 2, pp. 1092-1101, May 1994. K. Tomiyama, J.P. Daniel and S. Ihara, “Modeling air conditioner load for power system studies,” IEEE Trans. on Power Systems, vol. 13, no. 2, pp. 414-421, May 1998. K. Tomiyama, S. Ueoka and T. Takano, “Modeling of load during and after system faults based on actual field data,” IEEE PES General Meeting, July 2003, Toronto. H.W. Dommel, ElectroMagnetic Transients Program. Reference Manual (EMTP Theory Book), Bonneville Power Administration, Portland, 1986. IEEE Voltage Quality Working Group, “Recommended practice for the establishment of voltage sag indices,” IEEE P1564, Draft, March 2001. P.A. Gnadt and J.S. Lawler (Eds.), Automatic Electric Utility Distribution Systems, Prentice Hall, 1990. J. Key et al., “The design of power acceptability curves,” IEEE Trans. on Power Delivery, vol. 17, no. 3, pp. 828-833, July 2002. J.A. Martinez and J. Martin-Arnedo, “Voltage sag stochastic prediction using an electromagnetic transients program,” approved for publication in IEEE Trans. on Power Delivery. Can/Am EMTP Users Group, ATP Rule Book, 2002. J.A. Martinez, J. Martin-Arnedo and J.V. Milanovic, “Load modeling for voltage sag studies,” IEEE PES General Meeting, July 2003, Toronto. J.V. Milanovic, R. Gnativ and K.W.M. Chow, “The influence of loading conditions and network topology on voltage sags,” 9th ICHQP, October 2000. B. Khodabackhchian and G.T. Vuong, “Modeling a mixed residentialcommercial load for simulation involving large disturbances,” IEEE Trans. on Power Systems, vol. 12, no. 2, pp. 791-796, May 1997. M. Reformat, D. Woodford, R. Wachal and N.J. Tarko, “Nonlinear load modelling for simulation in time domain,” 8th ICHQP, vol. 1, October 1998.

VII. BIOGRAPHIES Juan A. Martinez was born in Barcelona (Spain). He is Profesor Titular at the Departament d'Enginyeria Elèctrica of the Universitat Politècnica de Catalunya. His teaching and research interests include Transmission and Distribution, Power System Analysis and EMTP applications. Jacinto Martin-Arnedo was born in Barcelona (Spain). He is currently a Ph.D. candidate at the Universitat Politècnica de Catalunya. His research interests include Power Quality studies using EMTP-type tools and Transient Analysis of Power Systems.