Master of Electric Engineering

Master of Electric Engineering

Thesis presented to

UNIVERSIDAD DE LOS ANDES

FACULTY OF ENGINEERING

DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING

By

Daniel Sebastián Restrepo Lara

Adaptive POD for Power System with High Wind Power Penetration

Level

ASESOR

Mario Alberto Ríos Mesías, PhD, Titular Profesor,

Universidad de los Andes

Bogotá, Colombia.

Adaptive POD for Power System 2

Content

1 Introduction .................................................................................................................... 5

2 Reactive Power Compensation ....................................................................................... 6

3 Model Reference Adaptive Control (MRAC) ................................................................ 8

3.1 MIT Rule .................................................................................................................. 9

3.2 Adjustment Mechanism ........................................................................................... 9

A. Fuzzyfication: ..................................................................................................... 10

B. Fuzzy Rule-base: ................................................................................................ 11

C. Inference Mechanism: ........................................................................................ 11

D. Defuzzyfication: ................................................................................................. 11

4 Test System .................................................................................................................. 12

4.1 HVDC line ............................................................................................................. 12

4.2 Modal Analysis ...................................................................................................... 15

4.3 POD Controller Design .......................................................................................... 15

4.4 MRAC Design ....................................................................................................... 17

5 Simulation Results ........................................................................................................ 21

5.1 Controller performance case 1 ............................................................................... 21

5.2 Controller performance case 2 ............................................................................... 23

6 Conclusions .................................................................................................................. 25

7 References .................................................................................................................... 25


Figure Index

Figure 1. Integration STATCOM and Wind Farm [13] ......................................................... 7

Figure 2. Diagram of MRAC (Adapted from [15] ) ............................................................... 8

Figure 3. Scheme for Fuzzy controller adapted from [21] ................................................... 10

Figure 4. Fuzzyfication example .......................................................................................... 10

Figure 5. Test System ........................................................................................................... 12

Figure 6. Control strategy for substation HVDC [27] .......................................................... 13

Figure 7. Single line diagram ............................................................................................... 13

Figure 8. Supplementary controller POD ............................................................................. 16

Figure 9. MRAC with POD regulator. ................................................................................. 18

Figure 10. ESS reference model ........................................................................................... 19

Figure 11. Fuzzy Logic Controller ....................................................................................... 20

Figure 12. Error .................................................................................................................... 20

Figure 13. Delta-error ........................................................................................................... 21

Figure 14. Surface of rules-based ......................................................................................... 21

Figure 15. Power Flow line fault inter-area (MRAC) .......................................................... 22

Figure 16. Power Flow fault line inter-area (POD) .............................................................. 22

Figure 17. Adaptive parameter case 1 .................................................................................. 23

Figure 18. Power Flow line fault line SLACK (MRAC) ..................................................... 23

Figure 19. Power Flow line fault line SLACK (POD) ......................................................... 24

Figure 20. Adaptive parameter case 2 .................................................................................. 24


Table Index

TABLE I. Requirements for the integration of non-synchronous energies. ........................... 5

TABLE II. Comparison SVC and STATCOM ...................................................................... 7

TABLE III. Electromechanical modes comparison ............................................................. 15

TABLE IV. Parameters of classic supplementary controller POD ...................................... 17


1 Introduction

In the last decade, the use of renewable energy has presented a significant increase in the total

installed capacity throughout the world, in response to reducing dependence on fossil fuels

and their global warming problems. Wind energy is one of the most promising renewable

energy. For example, the Colombian electricity system has 16.6 GW of installed capacity to

the SIN, of which 11 GW are hydraulic, 4.6 GW thermal and approximately 1 GW of smaller

plants. However, it is expected that by the year 2023 the Colombian electricity system will

present important changes in its energy matrix, integrating at least 1.6 GW of non-

synchronous generation1 that currently have a connection concept, of which 0.3 GW will

correspond to solar generation and 1.3 GW to wind generation. XM has identified three stages

for the implementation of the proposals, which are defined based on the percentage of variable

generation integration in the system (MW) [2].

The total installed capacity of this generation represents less than 15% of the

maximum daily demand for electrical power in the system. This level of integration in

MW of the variable generation does not generate a considerable impact on the system.

The total installed capacity of this generation is greater than or equal to 15% and is

less than 25% of the maximum daily demand for electric power. This level of

integration in MW of variable generation begins to be relevant for the system.

The total installed capacity of the variable generation represents 25% or more of the

maximum daily demand for electrical power. This integration level in MW of the

generation compromises the flexibility and stability of the system.

TABLE I shows the technical and operational requirements for each of the integration stages

previously stated. This project is focused on the technical requirement for stage 3. Because,

there are concerns about the impacts of the wind energy on overall power system stability.

The stability of a power system it is done through small signal analysis where is defined the

capacity of the power system to keep synchronism under perturbations [1]. The high wind

power penetration level decreases the damping of weak electromechanical modes.

Nevertheless, the dynamical respond depends on the technology of the Wind Farm, precisely

the technology of the turbine.

TABLE I. Requirements for the integration of non-synchronous energies.

Stage 1 Stage 2 Stage 3

Technical

requirements

Over-frequency and sub-

frequency control

capability, Voltage

control and PQ diagram.

frequency control

through inertial

emulation for centrally

dispatched wind plants.

POD function for non-

synchronous plants with a

capacity greater than or

equal to 100 MW.

Operative

requirements

3% reserve on all plants

dispatched centrally or

greater than 20 MW for

frequency control.

Secondary reserves

3% reserve on all plants

dispatched centrally and

percentage of primary

reserve required


Based in [3], the majority of wind farms have been based on constant-speed technology, but

with the increment of the Wind energy, the planning installations are adopting the variable-

speed technology due to its better energy capture, smoother operation, lower flicker, and

superior controllability. In [3]-[5] it is mentioned that one of the most usual types of variable

speed turbines corresponds to a double-fed induction generator (DFIG). This technology has

presented technical and economic advantages, but also presents problems with dynamic

interactions for the directly connection with the grid and through an electronic power

converter. For this reason, the modal analysis of power systems with Wind Farms based on

DFIG turbines seeks to identify the controller and networks parameters with a major impact

in the system with the participation factors. This analysis allows comparing the change of

weak electromechanical modes with high Wind Power Penetration Level. On the other hand,

for the intermittent nature of wind energy, the power output has randomness. For this reason,

the point of common coupling (PCC) presents more frequent change in voltage. Moreover,

the random behavior of wind speed can make the wind farm consume reactive power affecting

the quality, safe and stable operation of the grid [6], [7]. Because of this behavior, reactive

compensation is an inherent condition for the Wind Farm connection. Although, DFIG

technology could realize automatic power regulation. However, the Wind Farms have many

generation units which increase of complexity of reactive power output coordination, as a

result, it is necessary the use of reactive power compensation schemes [6].

The principal problem of a grid that presents weak electromechanical modes is that in the

event of contingencies or changes in the point of operation, the system can generate

oscillations and depended on the magnitude the system could lose synchronism. Thus, the

implementation of a supplementary controller is necessary. For example, in [1] was added a

classic POD in the control loop for reactive power. Nevertheless, the classic supplementary

controller could have presented inconvenient whit faults that cause a big change in the point

of operation of the system or long-distance power transmissions., different optimization

algorithms have been used for the tuning of parameters of the supplementary controls. For

example, a genetic algorithm is used as a technique of optimization for the tuning parameters

of supplementary controllers PSS and POD in FACTS devices. The time simulation result is

used as data input for the algorithm, so it is considered an offline optimization technique [8]-

[10]. Another technique of optimization corresponds to PSO (particle swarm optimization)

for the coordinated designing of the thyristor-controlled series capacitor (TCSC) damping

controller and power system stabilizer (PSS) in a multi-machine power system [11]. Whit the

use of these optimization algorithms the global optimum for the parameters change respect to

the fault condition or network conditions. Therefore, the system requires a control that selects

the parameters according to the contingency. Nevertheless, this paper proposes an adaptive

supplementary controller for increasing the damping of weak electromechanical modes by

local control directly on the selected reactive compensation device, due to coordination

problems.

2 Reactive Power Compensation

Oscillatory damping behavior is improved for DFIG based wind generators by FACTS

devices. However, it is necessary the selection between SVC and STATCOM devices


thinking about the improvement of the dynamic response as observed in [6]-[12]. The

differences are briefly introduced in TABLE II.

TABLE II. Comparison SVC and STATCOM

SVC STATCOM

Control scheme based on Thyristors Control schemes based on VSC

Fast response Real time response

Big losses Little loss

Great harmonics Small Harmonics

Low cost High cost

The more efficient reactive power compensation device corresponds to STATCOM, which

present better respond when the voltage is below the range of normal operation. Thus,

STATCOM is a better compensating device than SVC for stabilizing a system [12].

According to the last, the reactive compensation device selected is a STATCOM and the

integration whit the grid and Wind Farm can be seen in Figure 1.

Figure 1. Integration STATCOM and Wind Farm [13]

A STATCOM device is a great solution to improve the dynamic response of the system or

achieve a secure connection of non-synchronous energies. For example, the integration of

the Wind Farm and STATCOM coordinated between the positive and the negative sequences

of the grid voltage and evaluated the system in fault conditions [13]. On the other hand, the

STATCOM is an appropriate option for the integration of a non-synchronous system based


in solar and wind power source through the compensation device, avoiding that the random

behavior of the sources affects directly the network [14].

3 Model Reference Adaptive Control (MRAC)

Based on [15] the general idea of MRAC is to create a closed loop controller with parameters

that can be updated to change the response to the system. These are updated based on the

error between the system output and the model reference. The goal is for the parameters

change to optimum values that cause the plant response to follow the response of the

reference model. Figure 2 shows the scheme of MRAC.

Figure 2. Diagram of MRAC (Adapted from [15] )

In [16], [17] was demonstrated that the designed optimal MRAS-PSS is capable of

guaranteeing the robust stability and robust performance of the power system over

conventional PSS. On the other hand, the methodologies most used to ensure the convergence

of the parameters are the Lyapunov stability theory and the gradient method evaluated in [16]

and [15] respectively. However, this paper is focused on gradient method.

It is worth mentioning that there is no standard methodology to find the reference model. The

reference model is defined based on the desired characteristics of the output. However, the

searched reference model must share characteristics similar to the homologous control for

the system. Generally, the model reference is a second-order transfer function as seen in (1)

to be able to ensure the desired output characteristics, such as; settling time, rise time,

overshoot.

𝐾𝑝𝑆(𝑠 + 𝑏0)

𝑆2 + 𝑎1𝑆 + 𝑎0 (1)


3.1 MIT Rule

The MIT rule seeks to minimize a cost function expressed in terms of the error between the

output of the system and the reference model [18]. In this rule, the cost function is defined

as:

𝐽(𝜃) =1

2𝑒2(𝜃) (2)

Where 𝑒 indicates the error between output system and model reference and 𝜃 is the

adjustable parameter. This parameter is adjusted to minimize the cost function from the

sensibility of 𝜃 to move in a way of the negative gradient of 𝐽 as seen in (3).

𝑑𝜃

𝑑𝑡= −𝛾

𝑑𝐽(𝜃)

𝑑𝜃= −𝛾𝑒

𝑑𝑒

𝑑𝜃 (3)

Where 𝜕𝑒

𝜕𝜃 is called as the sensitivity derivative of the system [18]. Equation (3) shows how

the error is changing with the adjust of parameter 𝜃 and 𝛾 which is the adaptation gain of the

controller.

3.2 Adjustment Mechanism

The adjustment mechanism corresponds to the methodology used for the change of the

adaptive parameter looking for improvement the dynamic response of the system. In this

paper, the method selected was Fuzzy logic control. This control methodology has already

been used in POD supplementary controller. For example, [19] the fuzzy logic has been used

as an auxiliary damping signal based in angular frequency error and error derivate. The

control loop of the POD for DFIG was embedded in RSC (Rotor side converter). In another

example, fuzzy logic has been used as an auxiliary damping signal located on STATCOM

located at the midpoint of the transmission line [20]. On the other hand, fuzzy logic can also

be used as a methodology of tuning of the parameters of the supplementary control and AVR.

The terminal voltage in the bus is a great selection as one of the inputs because the controller

can be a voltage regulator. Nevertheless, the angle deviation is selected as another input to

guarantee the synchronism in the power system [21].


Figure 3. Scheme for Fuzzy controller adapted from [21]

Figure 3 shows the step-by-step scheme for a Fuzzy logic controller. A general description

is present as follows, [22]:

A. Fuzzyfication:

This step converts a crisp input into a fuzzy variable. For this conversion is necessary the

definition of the membership functions, whose standard shapes are Gaussian, trapezoidal and

triangular. This is an independent process for each input and the idea is to transform an input

value into a vector of weights associated with the different membership functions. Figure 4

shows an example of fuzzification of service (input) and 3 membership functions classified

in poor, good and excellent. For input of 7 in service, (4) shows the vector of weights

associated.

[0 0.4111 0.1353] (4)

Figure 4. Fuzzyfication example


B. Fuzzy Rule-base:

The base of fuzzy rules is called the linguistic model of the control process, which includes

information about:

Regular and possible values of state variables.

The desired progress of the process.

the method applied to bring and keep the process at the required level.

The Fuzzy Rule-base is based on a set of if-else rules that related the inputs with the outputs.

C. Inference Mechanism:

Mamdani and Sugeno are the most frequently used model based on the fuzzy inference.

Below is shown the comparison between inference mechanism Mamdani and Sugeno [23].

The mechanism inference selected correspond to Takagi-Sugeno for the advantages in the

adaptive techniques.

MAMDANI

Are intuitive.

Have widespread acceptance.

Are well-suited to human input.

Easy formalization and interpretability.

Can be used for both MISO and MIMO systems.

Output can either be fuzzy or a crisp output.

TAKAGI-SUGENO

Are computationally efficient.

Work well with optimization and adaptive techniques.

Guarantee continuity of the output surface.

More robust when in presence of noisy input data such as sensor data.

Allowed more degrees of freedom and more flexibility in the design.

Continuous structure of output function

D. Defuzzyfication:

The main difference among inference mechanisms exposed above is the defuzzification

process. Mamdani model converts the output Fuzzy variable into a unique number using

different methods. The most popular method corresponds to Centroid that is a weighted

average. On the other hand, Takagi-Sugeno model is the functional and continuous

relationship between inputs and outputs considering the activation of individual conclusions.

The defuzzyfication expression for Sugeno model is observed in (5).

𝑍 =∑ 𝑤𝑖 ∙ 𝑓𝑖(𝑥, 𝑦)𝑛

𝑖=1

∑ 𝑤𝑖𝑛𝑖=1

(5)


Where 𝑤𝑖 is the min{𝜇𝐴𝑖(𝑥), 𝜇𝐵𝑖

(𝑦)} , being A and B the fuzzy variable corresponding to

inputs. 𝑓𝑖(𝑥, 𝑦) is the function of each rule for example, 𝑖𝑓 𝑥 𝑖𝑠 𝐴1 𝑎𝑛𝑑 𝑦 𝑖𝑠 𝐵1 → 𝑓1(𝑥, 𝑦).

𝑍 is the output of Sugeno model.

4 Test System

The test system is an adaptation of the Kundur system of two areas taken from [24].

Additionally, the system has a VSC-HVDC line based in [25] for control strategies. This

system has 3 synchronous machines of 900 MVA and one Wind Farm of 900 MVA that

correspond to 25 percent of total installed capacity without power transmission by HVDC.

The Wind Farm is compound for 180 DFIG turbines each 5MW. There is a new generator of

900 MW, which transmitted 600 MW by the HVDC connection that is connected to bus 9.

To achieve this transmission, the load in bus 9 has an increase of the same magnitude.

Besides, the generator 2 has a PSS as a supplementary controller to get an individual control

of the two areas. The lines between the buses 7 and 9 transport 400 MW to area 2. Figure 5

shows the full test system. Dynamic simulation and test of the controllers are performed in

Power Factory DigSilent.

Figure 5. Test System

4.1 HVDC line

One of the most used controllers for the control of a substation based on VSC-HVDC

technology corresponds to the control by the vectorial method, which is based on simplifying

the representation the three-phase system through a DQ transformation. Figure 6 shows the

vector control scheme used for the control of substations.

The PLL block measures the frequency of the system and calculates a synchronization angle

𝜃 used for the DQ transform. In steady state sin 𝜃 is in phase with the fundamental component

(sequence positive) of phase A voltage, this means that if the axes dq are correctly aligned,

the component 𝑣𝑞 is equal to 0. The instantaneous information of the angle is necessary for


the control independent of the active power and the reactive power, to facilitate the

approximation of the angle of synchronization on the Clark transform [27].

𝜃 = tan−1 (𝑣𝛽

𝑣𝛼) (6)

Figure 6. Control strategy for substation HVDC [27]

Figure 7. Single line diagram

Figure 7 shows the single line diagram, from the figure it is known that:

𝑣𝑠 = 𝑅𝑖𝑠 + 𝐿𝜕𝑖𝑠

𝜕𝑡+ 𝑣𝑐 (7)


Applying the dq transform you have to

[𝑣𝑠,𝑑

𝑣𝑠,𝑞] = 𝑅 ∗ [

𝑖𝑑

𝑖𝑞] + 𝐿

𝜕

𝜕𝑡[𝑖𝑑

𝑖𝑞] + 𝐿 [

0 −𝜔𝜔 0

] [𝑖𝑑

𝑖𝑞] + [

𝑣𝑠,𝑑

𝑣𝑠,𝑞] (8)

The dynamics of the system are

𝐿𝜕𝑖𝑑

𝜕𝑡= −𝑅𝑖𝑑 + 𝜔𝐿𝑖𝑞 − 𝑣𝑐,𝑑 + 𝑣𝑠,𝑑

𝐿𝜕𝑖𝑞

𝜕𝑡= −𝑅𝑖𝑞 + 𝜔𝐿𝑖𝑑 − 𝑣𝑐,𝑞 + 𝑣𝑠,𝑞

(9)

Rewriting the previous expressions, you have to

𝐿𝜕𝑖𝑑

𝜕𝑡+ 𝑅𝑖𝑑 − 𝐿𝑖𝑞 = −𝑣𝑐,𝑑 + 𝑣𝑠,𝑑

𝐿𝜕𝑖𝑞

𝜕𝑡+ 𝑅𝑖𝑞 − 𝜔𝐿𝑖𝑑= − 𝑣𝑐,𝑞 + 𝑣𝑠,𝑞

(10)

From the previous equations, it can be observed that the model of the VSC converters in the

coordinate axis dq is a non-linear MIMO system (multiple inputs and multiple outputs), In

addition, a derivative term corresponding to a cross coupling between the two axes is

presented. This cross coupling can be considered as a disturbance from the control point of

view. In order to achieve better performance, a PI current regulator is added to improve the

response in steady state of the system. To uncouple the controller from axes d and q, the

output of each controller corresponds to the reference voltage of each axis.

𝐹(𝑠) = 𝑘𝑝 +𝑘𝑖

𝑠 (11)

𝑣𝑐,𝑑𝑟𝑒𝑓

= (𝑖𝑑,𝑟𝑒𝑓 − 𝑖𝑑)𝐹(𝑠) + 𝜔𝐿𝑖𝑞 + 𝑣𝑠,𝑑

𝑣𝑐,𝑞𝑟𝑒𝑓

= (𝑖𝑞,𝑟𝑒𝑓 − 𝑖𝑞)𝐹(𝑠) + 𝜔𝐿𝑖𝑑 + 𝑣𝑠,𝑞

(12)

Combining equations (10) and (12) respectively in the domain of Laplace you get

𝑣𝑐,𝑑𝑟𝑒𝑓

= (𝑖𝑑,𝑟𝑒𝑓 − 𝑖𝑑)𝐹(𝑠) + 𝜔𝐿𝑖𝑞 + 𝑣𝑠,𝑑 + 𝐿𝑠𝑖𝑑 + 𝑅𝑖𝑑 − 𝜔𝐿𝑖𝑞 + 𝑣𝑐,𝑑

𝑣𝑐,𝑞𝑟𝑒𝑓

= (𝑖𝑞,𝑟𝑒𝑓 − 𝑖𝑞)𝐹(𝑠) + 𝜔𝐿𝑖𝑑 + 𝑣𝑠,𝑞 + 𝐿𝑠𝑖𝑞 + 𝑅𝑖𝑞 − 𝜔𝐿𝑖𝑑 + 𝑣𝑐,𝑞

(13)

From the above it is obtained that

𝐺(𝑠) =1

𝐿𝑠 + 𝑅 (14)

𝑖𝑑 = (𝑖𝑑,𝑟𝑒𝑓 − 𝑖𝑑)𝐹(𝑠)𝐺(𝑠)

𝑖𝑞 = (𝑖𝑞,𝑟𝑒𝑓 − 𝑖𝑞)𝐹(𝑠)𝐺(𝑠)

(15)


Therefore, it is possible to conclude that the current controllers are completely independent

for each axis.

4.2 Modal Analysis

TABLE III shows a comparison of electromechanical modes between the system whit 25

percent of wind energy and the system with all generators as a synchronous machine. It is

important to clarify that the electromechanical modes are those that have a frequency

oscillation between 0.5 and 3 Hz. On the other hand, a damping percentage of less than 20%

is assumed for a mode to be considerable. TABLE III shows that the high penetration level

of wind energy presents a significant change in the inter-area electromechanical mode. This

mode presents positive real part which makes it unstable.

TABLE III. Electromechanical modes comparison

All generators synchronous machine

Mode Eigen Value Frequency (Hz) Damping 𝜻(%)

Area 1 -0.5395±6.7135 1.0685 8.01

Area 2 -0.6843±6.9959 1.1134 9.74

Inter-area -0.7476±3.5194 0.5601 20.78

Penetration level wind energy 25 percent

Mode Eigen Value Frequency (Hz) Damping 𝜻(%)

Area 1 -0.6318±6.7348 1.0719 9.34

Area 2 -1.2176±17.6447 2.8082 6.88

Inter-area 0.1023± 3.5527 0.5654 -2.88

4.3 POD Controller Design

The structure of the supplementary controller POD is shown in Figure 8, this structure has a

proportional gain, a washout filter and a phase lead-lags filter [26].


Figure 8. Supplementary controller POD

Based on [26], the washout filter acts like a low-pass filter that prevents changes in the

frequency, speed or power flow that can affect the voltages. A washout time constant of 10

seconds is desirable for inter-area oscillations. For the case of the lead-lags filters, it is

recommendable to select their constants in function of a compensation angle. Where is the

exponent for the washout filter that takes a value of 1 if the input signal of the POD is the

rotor speed. On the other hand, n is the exponent for the lead-lags filter for a compensation

angle less than 45°. The parameters of the controller are α, the pole (𝑇2) and the zero (𝑇1),

were calculated from the following equations:

𝜙𝑚 =180° − Θ𝑑𝑒𝑝

𝑛 (16)

𝛼 =1 + sin 𝜙𝑚

1 − sin 𝜙𝑚 (17)

𝑇2 = √𝛼𝜔𝐶 (18)

𝑇1 =𝑇2

𝛼 (19)

Where ∅𝑚, 𝜃𝑑𝑒𝑝 and 𝜔𝑐 represents the required compensation phase, the output angle of the

inter-area mode and the mode frequency in rad / s, respectively. TABLE IV shows the

parameters of the supplementary controller POD for the inter-area mode with a 25 percent

penetration level of wind energy presented in TABLE III.


TABLE IV. Parameters of classic supplementary controller POD

Parameter Value

m 1

n 2

𝚯𝒅𝒆𝒑 88.3509

𝝓𝒎 45.8246

𝜶 6.0724

𝑻𝟐 8.7545

𝑻𝟏 1.4417

Tw 10

K 200

4.4 MRAC Design

The error between the model reference and the plant can be observed in

𝑒(𝑡) = 𝐺𝑝(𝑡)𝑈𝑐(𝑡) − 𝐺𝑚(𝑡)𝑈(𝑡) (20)

Where, 𝐺𝑝, 𝐺𝑚 correspond to the function that describes the behavior plant and the behavior

model reference respectively. Besides, 𝑈𝑐(𝑡) = 𝜃(𝑡) ∗ 𝑈(𝑡) where 𝜃(𝑡) is the adaptive

parameter. The error can be rewritten in Laplace form as in (21).

𝑒(𝑠) = 𝐺𝑝(𝑠) ∗ 𝑈(𝑠) − 𝐺𝑚(𝑠) ∗ 𝑈(𝑠) ∗ 𝜃(𝑠) (21)

Based in the supplementary controller POD, Equation (22) shows the adaptive controller

𝜃(𝑠).

𝜃(𝑠) = (𝐾𝑠𝑇𝑤

1 + 𝑠𝑇𝑤 (𝛼

1 + 𝑠𝑇1

1 + 𝑠𝑇2)

2

) (22)

Where 𝐾 is the adaptive parameter and the data to change. Replacing (22) in (21).

𝑒(𝑠) = 𝐺𝑝(𝑠)𝑈(𝑠) (𝐾𝑠𝑇𝑤

1 + 𝑠𝑇𝑤 (

1 + 𝑠𝑇1

1 + 𝑠𝑇2)

2

) − 𝐺𝑚(𝑠)𝑈(𝑠) (23)


The derivative of sensitivity is obtained by deriving the controller with respect to the

adaptive parameter.

𝛿𝑒(𝑠)

𝛿𝐾(𝑠)= (

𝑠𝑇𝑤

1 + 𝑠𝑇𝑤) (

1 + 𝑠𝑇1

1 + 𝑠𝑇2)

2

(24)

Next, the MIT rule is applied.

𝑠 ∗ 𝐾(𝑠) = −𝛾 ∗ 𝑒(𝑠) ∗ (𝑠𝑇𝑤

1 + 𝑠𝑇𝑤) (

1 + 𝑠𝑇1

1 + 𝑠𝑇2)

2

(25)

Equation (26) is obtained by clearing the adaptive gain from (25).

𝐾(𝑠) = −𝛾 ∗ 𝑒(𝑠) ∗ (𝑇𝑤

1 + 𝑠𝑇𝑤) (

1 + 𝑠𝑇1

1 + 𝑠𝑇2)

2

(26)

Figure 9 shows the model reference adaptive controller based in a POD regulator. Where 𝛾

is the adaptive gain.

Figure 9. MRAC with POD regulator.

On the other hand, the reference model is based on the second-order transfer function shows

in (27). How the damping of the most unstable mode is negative, it is necessary that the

reference model does not present a damping of more than 9% because it requires a greater

effort in the turbine and a greater inertial mass.

𝑦𝑚 =𝜔𝑛

2

𝑠2 + 2𝜁𝜔𝑛𝑠 + 𝜔𝑛2 (27)

The frequency of the unstable mode was 0.5654 Hz. whit this is possible calculated the peak

time as in (18)


𝑡𝑝 =1

𝑓𝑜𝑠𝑐≈ 1.7686 [𝑠] (28)

The peak time and the damping selected were used for the calculation of oscillation frequency

and the establishment time of the reference model as it is presented in the following.

𝜔𝑛 =𝜋

𝑡𝑝 ∙ √1 − 𝜁2= 1.7846 [

𝑟𝑎𝑑

𝑠] (29)

𝑡𝑠 =4

𝜁 ∙ 𝜔𝑛= 24.9189 [𝑠] (30)

Replacing 𝜔𝑛 and 𝜁 in (27), the transfer function is shown in (31).

𝑦𝑚 =3.1811

𝑠2 + 0.3210𝑠 + 3.1811 (31)

Equation (32) shows the eigenvalues of reference model present a positive real part, which

implies that the damping is positive.

𝜆1,2 = −0.1605 ± 𝑖1.7763 (32)

Besides, is necessary add a gain of 𝑘𝑝 = 1 ∗ 10−3 so that the output resembles the

response of a synchronous machine.

𝑦𝑚 =3.1811 ∗ 10−3

𝑠2 + 0.3210𝑠 + 3.1811 (33)

Figure 10 shows the error stationary state of the reference model. It is important that the

establishment time is congruent on the value found previously.

Figure 10. ESS reference model


Figure 11 shows the Fuzzy logic controller selected for this paper. The controller is

compound for two inputs that corresponding to error and derivate of error of the frequency

in the bus 9. The rule-based has 81 rules according to 9x9 Fuzzyfication inputs. For a better

solution, the tuning of Sugeno model is possible through the tool “Anfis” of matlab.

Figure 11. Fuzzy Logic Controller

Figure 12 and Figure 13 show the Fuzzyfication schemes for the inputs in the Fuzzy

system. Additionally, Figure 14 shows the surface that related the inputs with the output

based on the rule-based.

Figure 12. Error


Figure 13. Delta-error

Figure 14. Surface of rules-based

5 Simulation Results

In order to compare the supplementary control of the MRAC based in a regulatory POD and

the classic POD, there are two cases to measure their performances.

5.1 Controller performance case 1

In the first case, the system is subjected to a three phases fault at a time of 0.5 s on the line

8-9A and the failure clearance 5 cycles after. Figure 15 and Figure 16 show the power flow

in the line 7-8A and 7-8B whit the MRAC and POD supplementary controller respectively.

It is possible to observe that a POD controller presents less error in the stationary state than

the MRAC controller. Nevertheless, the overshoot of the MRAC controller is lower. On the

other hand, the establishing time is approximately the same.


Figure 15. Power Flow line fault inter-area (MRAC)

Figure 16. Power Flow fault line inter-area (POD)

Figure 17 shows the change of the adaptive parameter γ through time. The time interval is of

6 to 12 seconds because the initial values present great magnitude and the parameter after 4

seconds appears to be zero. It is possible to observe that the data tends to stabilize close to

20.


Figure 17. Adaptive parameter case 1

5.2 Controller performance case 2

In the second case, the system is subjected to a three phases fault at a time of 0.5 s on the line

10-11A and the failure clearance 5 cycles after. It is important to clarify that this line connects

the slack node with the rest of the system. Figure 18 and Figure 19 shows the power flow in

the line 7-8A and 7-8B whit the MRAC and POD supplementary controller respectively.

Figure 18. Power Flow line fault line SLACK (MRAC)


Figure 19. Power Flow line fault line SLACK (POD)

It is possible to observe that a POD controller is unable to maintain the stability of the

system for the proposed failure. On the other hand, the MRAC controller presents large

oscillations but maintains the stability of the system after the second 6. Figure 20 shows the

change of the adaptive parameter γ through time. Figure 20 shows that the value presents

more oscillations in comparison whit case 1, but tends to a set point.

Figure 20. Adaptive parameter case 2


6 Conclusions

It is important to highlight that the Small-Signal Stability was the main analysis to

demonstrate that the high penetration of wind energy considerably affects the damping of the

most unstable mode by the low inertia of the turbine and the random behavior of the wind.

Besides, it was important to clarify the need to STATCOM as a reactive power compensation

for the complexity of coordinated the reactive output of all the turbines.

This paper had proposed a methodology for design and implementing a supplementary

controller on a STATCOM connected in the point of common coupling whit the Wind Farm

and the network. It was demonstrated that an adaptive supplementary control by a reference

model based on a POD regulator presents better results than a classic POD regulator based

on a SISO system. It is important to clarify that a comparison was made between the two

most commonly used inference mechanisms for Fuzzy controller to determine the

mechanism that best suits the needs of an adaptive control. Besides, the supplementary

control was probed in three-phase fault inter-area and three-phase fault line that connect the

Slack generator. This last fault is the most critical for the system according to the results.

Future extension to this work could be the implementation of a methodology for the tuning

the Sugeno model because the data training was selected for multiple tests made to the system

and taking the data of the best results. Which does not ensure a global optimum in the

adaptive parameter. Furthermore, the Wind Farm could replace the generator 5 in order to

evaluate the effect of an HVDC connection that presents a random behavior. On the other

hand, future work may also be to apply the methodology to an equivalent Colombian

transmission system. In order to verify the feasibility of each of the stages proposed by XM.

7 References

[1] A. Arvani and V. S. Rao “Power oscillation damping controller for the power system

with high wind power penetration level,” in Proc. 2014 North American Power

Symposium (NAPS)., pp. 1-6.

[2] XM, Centro Nacional de Despacho, "PROPUESTA DE REQUERIMIENTOS

TÉCNICOS PARA LA INTEGRACIÓN DE FUENTES DE GENERACIÓN NO

SÍNCRONA AL SIN," Bogotá, 2017.

[3] A. Ostadi, A. Yazdani and R. K. Varma, "Modeling and Stability Analysis of a DFIG-

Based Wind-Power Generator Interfaced With a Series-Compensated Line," in IEEE

Transactions on Power Delivery, vol. 24, pp. 1504-1514, July 2009.

[4] X. He, H. Geng, G. Yang, X. Zou and Y. Li, "Equivalent modelling of wind farm for

small-signal stability analysis in weak power system," in The Journal of Engineering, vol.

2017, pp. 1388-1393, 2017.

[5] L. Fan, C. Zhu, Z. Miao and M. Hu, "Modal Analysis of a DFIG-Based Wind Farm

Interfaced With a Series Compensated Network," in IEEE Transactions on Energy

Conversion, vol. 26, pp. 1010-1020, Dec. 2011.


[6] A. Pandey and A. K. Pandey, "Reactive power compensation for a doubly fed induction

generator based WECS," 2017 International Conference on Innovations in Information,

Embedded and Communication Systems (ICIIECS), pp. 1-4.

[7] R. C. Duan, F. H. Wang, Z. B. Ling and Z. J. Jin, "Dynamic optimal reactive power

compensation control strategy in wind farms of DFIG," 2013 IEEE Power & Energy

Society General Meeting, pp. 1-5.

[8] S. Keskes, N. Bouchiba, S. Sallem, L. Chrifi-Alaoui and M. B. A. Kammoun, "Optimal

tuning of power system stabilizer using genetic algorithm to improve power system

stability," 2017 International Conference on Green Energy Conversion Systems (GECS),

pp. 1-5.

[9] H. T. Canales, F. C. Torres and J. C. S. Chávez, "Tuning of power system stabilizer PSS

using genetic algorithms," 2014 IEEE International Autumn Meeting on Power,

Electronics and Computing (ROPEC), pp. 1-6.

[10] R. Narne, P. C. Panda and J. P. Therattil, "Genetic algorithm based simultaneous

coordination of PSS and FACTS controllers for power oscillations damping," 2012 IEEE

Third International Conference on Sustainable Energy Technologies (ICSET), pp. 85-90.

[11] H. Shayeghi, A. Safari, H. A. Shayanfar, “PSS and TCSC damping controller coordinated

design using PSO in multi-machine power system,” in Energy Conversion and

Management, Volume 51, Pages 2930-2937, Dec. 2010.

[12] S. Bagchi, S. Goswami, R. Bhaduri, M. Ganguly and A. Roy, "Small signal stability

analysis and comparison with DFIG incorporated system using FACTS devices," 2016

IEEE 1st International Conference on Power Electronics, Intelligent Control and Energy

Systems (ICPEICES), pp. 1-5.

[13] S. Ahsan, A.S. Siddiqui, " Dynamic compensation of real and reactive power in wind

farms using STATCOM," in Perspectives in Science, vol. 8, pp. 519-521, July 2016.

[14] P. M. Chavan and G. P. Chavan, "Interfacing of hybrid power system to grid using

statcom & power quality improvement," 2017 International Conference on Information,

Communication, Instrumentation and Control (ICICIC), pp. 1-5.

[15] F. Parandin, A. Mohammadi, H. Sariri, “Adaptive Multi Machine PSS Design for Low

Frequency Oscillations Damping,” in Indian Journal of Science and Technology, Volume

5, Pages 64-68, Dec. 2012.

[16] R. Hemmati, “Power system stabilizer design based on optimal model reference adaptive

system,” in Ain Shams Engineering Journal, Volume 9, Pages 311-318, June 2018.

[17] F. Parandin, A. Mohammadi, H. Sariri and I. G. Branch, “Power System Stabilizer Design

based on Model Reference Adaptive System,” in Journal of American Science, Volume

8, Pages 751-755, 2012.


[18] M. Swathi and P. Ramesh, "Modeling and Analysis of Model Reference Adaptive

Control by Using MIT and Modified MIT Rule for Speed Control of DC Motor," 2017

IEEE 7th International Advance Computing Conference (IACC), pp. 482-486.

[19] R. Effatnejad, A. Zare, K. Choopani and M. Effatnejad, "DFIG-based damping controller

design to damp low frequency oscillations in power plant industry," 2016 International

Conference on Industrial Informatics and Computer Systems (CIICS), pp. 1-5.

[20] M. R. Safari Tirtashi, A. Rohani and R. Noroozian, "PSS and STATCOM controller

design for damping power system oscillations using fuzzy control strategies," 2010 18th

Iranian Conference on Electrical Engineering, pp. 901-906.

[21] R. Khezri and H. Bevrani, "Fuzzy-based coordinated control design for AVR and PSS in

multi-machine power systems," 2013 13th Iranian Conference on Fuzzy Systems (IFSC),

pp. 1-5.

[22] W. Z. Chmielowski, “Fuzzy Control in environmental engineering,”, Ed. Spronger, 2016,

pp. 3-34.

[23] A. Hamam and N. D. Georganas, "A comparison of Mamdani and Sugeno fuzzy

inference systems for evaluating the quality of experience of Hapto-Audio-Visual

applications," 2008 IEEE International Workshop on Haptic Audio visual Environments

and Games, pp. 87-92.

[24] R. Ramos, I. Hiskens and others, “Benchmark Systems for Small-Signal Stability

Analysis and Control,” IEEE Power & Energy Society, Tech. Rep. PES-TR18, Aug.

2015.

[25] O. Lennerhag, V. Träff, “Modelling of VSC-HVDC for Slow Dynamic Studies,

Gothenburg,” Sweden: Master's Thesis, Department of Energy and Environment,

Chalmers University of Technology, 2013.

[26] P. Kundur, “Power System Stability and Control,” Ed. McGraw-Hill, 1994.

[27] Daniel Sebastián Restrepo Lara. “Estudio de fallas y planteamiento de protecciones para

sistemas de alta potencia basados en tecnología VSC-HVDC”. Graduation project,

Universidad de los Andes, 2017

Master of Electric Engineering

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