power system load modelling

HOCHIMINH CITY UNIVERSITY OF TECHNICAL EDUCATIONFaculty of Electrical & Electronics Engineering

POWER SYSTEM LOAD MODELLING

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OBJECTIVES

Introduce the mathematical model for loads.

Different types of Static and Dynamic Load Models.

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CONTENTS

Part 1: Description of a power system.Part 2: Overview of modelling.Part 3: Different types of static and dynamic load models.Part 4: Conclusion.

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PART 1:DESCRIPTION OF A POWER SYSTEM

1.1. Description of a power system 1.2. Load classification1.3. Signification of load modelling

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The power system is subdivided into

(LOADS)

1.1. DESCRIPTION OF A POWER SYSTEM

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LOADS

INDUSTRIAL

RESIDENTIAL

COMMERCIAL

AGRICULTURAL

1.2. LOAD CLASSIFICATION

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INDUSTRIAL LOADS

Industrial processes

Up to 95%

Heavy industrial


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RESIDENTIAL LOADS

Domestic users

lightingrefrigerator

fan

televisionair conditioner

electric heating


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COMMERCIAL LOADS

Discharge

Lighting

Air conditionerEscalator


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AGRICULTURAL LOADS

Induction motors


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Power system load is complicatedThe exact composition of load is difficult to estimateThe composition changes depending on time, weather conditions, state of the economy…

Figure 1: Power system configuration identifying parts of the system represented as load at a bulk power delivery point

1.3. SIGNIFICATION OF LOAD MODELLING

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PART 2:OVERVIEW OF MODELLING

2.1. What is model ?2.2. Load models2.3. Load modelling approaches2.4. Applications of modelling

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A model is a set of equations to describe the relationship between the input and output of a system.

2.1.WHAT IS MODEL ?

equations

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Load models express the characteristic of the load as algebraic functions of the bus voltage magnitude and frequency, and the power consumed by the load: active and reactive.

2.2. LOAD MODEL

fv

ooo f

fVVPP

Ex:

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2.3. LOAD MODELLING APPROACHES

There are essentially two approaches to the determination of system load characteristics: - Component based - Measurement basedThe component based approach lends itself more readily to model generalization

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2.3. LOAD MODELLING APPROACH

Each load component type is tested to determine the relationship between real and reactive power requirements versus applied voltage and frequency.

Component based approach (bottom – up approach)

A load model is developed from the respective test data (poly or exp form).

The load model is expressed on a per – unit basic.

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Component based approach (bottom – up approach) Bulk power

delivery pointBus load

Load class mix

Load component

Component characteristics

Industrial Commercial Residential Agricultural….

Space heater Water heater Air conditioner Lighting Refrigeration

Power factor P(V,f) Q(V,f) More parameters

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Measurement based approach (top – down approach) Measurements are taken at either a substation and feeders, some load aggregation point along a feeder, or at some individual load point at selected times of the day and season

Variation of frequency is not usually performed. Voltage is varied and the measured real and

reactive power consumption recorded. Statistical methods are then used to determine

load models.

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Measurement based approach (top – down approach)

WW WW

Switch caps

LOAD LOAD

Typically 12.5 kV

Typically 115 kV

Figure 2: Typical station configuration for testing load characteristics

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conclusion The component test method was used to

characterize individual load components, used in simulation studies.

The measurement method was used to an aggregate of actual loads to verify and validate the component method.

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2.4. APPLICATIONS OF LOAD MODEL

Static applications:

The applications are divided into two broad categories: Static and dynamic

Power flow (PF).

Voltage stability (VS)

Distribution power flow (DPF) Harmonic power flow (HPF) Transmission power flow (TPF)

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Dynamic applications:

The applications are divided into two broad categories: Static and dynamic

Transient stability (TS) Dynamic stability (DS) Operator training simulators (OTS)

2.4. APPLICATIONS OF LOAD MODEL

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PART 3:DIFFERENT TYPES OF

STATIC AND DYNAMIC LOAD MODELS

3.1. Static Load models3.2. Dynamic Load models

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3.1. STATIC LOAD MODELS

- Static load model is not dependent on time.

- A static model expresses the characteristics of the load at any instant of time as algebraic functions of the bus voltage magnitude and frequency at that instant.

- Used for a long time for both purpose: Represent static load components, Approximate dynamic components.

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Parameters.

0

0pv

VV

PP

k

0

0qv

VV

QQ

k

0

0pf

ff

PP

k

0

f

0qf

f

QQ

k

Where:- P0, Q0, f0, V0 are active and reactive power, frequency, voltage at the initial opearting condition.- kpv, kqv, kpf, kqf are the voltage and frequency sensitivity parameters of the model.

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a. Constant impedance load model.The power varies directly with the square of the voltage magnitude.

2

00 V

VPP

2

00 V

VQQ

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b. Constant current load model.The power varies directly with the voltage magnitude.

00 V

VPP

00 V

VQQ

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c. Constant power load model.The power does not vary with changes in voltage magnitude.

0PP 0QQ

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d. Polynomial load model.This is a static load model that represents the power relationship to voltage magnitude as a polynomial equation.

This model is sometimes referred to as the ZIP model, as it is composed of constant impedance (Z), constant current (I) and constant power (P) components.

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d. Polynomial load model.

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02

2

010 a

VVa

VVaPPEquation:

Where:

When using these models for representing a bus load P0, Q0, f0, V0 are active and reactive power, frequency, voltage at the initial opearting condition.

- a1...a6: parameters of this model, which define the proportion of each component. a1 + a2 + a3 = a4 + a5 + a6 =1- Vo is the rated voltage of the device.Po, Qo are active and reactive power consumed at rated voltage.

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05

2

040 a

VVa

VVaQQ

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e. Exponential load model.


This is a static load model that represents the power relationship to voltage as an exponential equation.

np

00 V

VPP

Equation:

nq

00 V

VQQ

- np and nq are parameters of this model. With these exponents equal to 0, 1, or 2, the model represents constant power, constant current, or constant impedance chracteristics, respectively.

Where:

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e. Exponential load model.

Other exponents can be used to represent the aggregate effect of different types of load components.

Table 3.1: Parameters for voltage dependencies of Static Loads

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f. Frequency dependent load model.

The frequency denpendency of load characteristics is usually represented by multiplying the exponential model or the polinomial model by a factor.[1 + Kpf.Δf] [1 + Kqf.Δf]

- Δf is the frequency sensivity parameter of this model Δf= f – f0 With: f is the frequency of the bus voltage and f0 is the rated frequency.

- Kpf & Kqf is the frequency sensitivity parameter

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f.K1VVPP pf

np

00

f.K1VVQQ qf

np

00

f.K1aVVa

VVaPP pf3

02

2

010

f.K1aVVa

VVaQQ qf3

02

2

010

Equation: Where:

- P0, Q0, V0 are active and reactive power, voltage at the initial opearting condition- np and nq are parameters of this model. - Kpf is the active power frequency

damping coefficient.- Kqf is the reactive power frequency

damping coefficient.


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g. Combine Exponential and Polynomial model.Exponential and Polynomial models may be combined to form a synthesized static model that offers greater flexibility in representing various load characteristics.


P = P0[PZIP + PEX1 + PEX2]

3

02

2

01ZIP a

VVa

VVaP

f.K1VVaP 1pf

1np

041EXP

f.K1VVaP 2pf

2np

052EXP

Where:

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conclusion

Constant impedance load model Constant current load model Constant power load model Polynomial load model Exponential load model Frequency dependent load model Combine exponential and polynomial model

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3.2. DYNAMIC LOAD MODELS

Dynamic load model expresses the active and reactive powers at any instant of time as functions of the voltage manitude and frequency at the past instance of time and usually, including the present instant.

When the traditional static load models are not sufficient to represent the behavior of the load, the dynamic load models are necessary.

Using measurement based or component based approach to determine parameters.

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Equation: ts

00

00tsr

rp V

VPVVP)V(P)V(PP

dtdPT

t

00rl V

VPPP

- Tp : the active power recovery time constant.- Pr : the active power recovery.- P0 : the initial value of active power before the voltage change.- V0 : initial voltage value.- αs: the steady state active power voltage exponent.- αt: the transient active power voltage exponent.- PL the active power consumption

Where:

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Equation: ts

00

00tsr

rq V

VQVVQ)V(Q)V(QQ

dtdQT

t

00rl V

VQQQ

- Tq : the reactive power recovery time constant.- Qr : the reactive power recovery.- Q0 : the initial value of reactive power before the voltage change.- V0 : initial voltage value.- βs: the steady state reactive power voltage exponent.- β t: the transient reactive power voltage exponent.- QL the reactive power consumption

Where:


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Figure 3: Load response under ΔU step, from the U0 level

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PART 4:CONCLUSION

4.1. Conclusion4.2. Limits4.3. Future development4.4. References4.5. Contact

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4.1 ConclusionThis report has fulfilled its intend objectives of investigating different types of load modeling

4.2 Limits

Load modeling is not deeply researchMost contents are theoretical analysis, no simulation has been done

4.3 Future development

The dynamic load model should be studiedModelling of induction motors

CONCLUSION

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4.4 References

2. Prabha Kundur, Power System Stability and Control, McGraw-Hill, Newyork, 271–314, 1994.

4.5 ContactNguyen Phat LoiEmail: [email protected]: 0975.828.428

CONCLUSION

3. William H.Kersting, Distribution System, New Mexico State University.

1. Masoud Babazadeh, The lastest development on dynamic load modelling in power system, Monash University, Australia.

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Thank you for attending

power system load modelling

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