MIMO-PID Controller for Deregulated Environment

transcript

MIMO-PID CONTROLLER FOR

DEREGULATED ENVIRONMENTPRESENTED BY

MALLEM PRADEEP KUMAR12191D0716

UNDER ESTEEMED GUIDANCE

Sri K. VIMALA KUMAR M.Tech., (Ph.D.)ASSISTANT PROFESSOR

Department of Electrical & Electronics EngineeringJ N T U A COLLEGE OF ENGINEERING PULIVENDULA

OBJECTIVE

A novel decentralized MIMO-PID (Multi Input Multi Output-Proportional Integral Derivative) Controller is proposed.

Amenable to practical implementations.

Used LMI (Linear Matrix Inequalities) algorithm for three area power system.

Objective is to minimize transient deviations in area frequency and tie-line power in system.

H∞ norm used for improving robustness of the system and to achieve stabilization in system.

Proposed controller is named as MIMO-PIDH∞ controller.

Even though H∞ control is high-order system but designed for stability of overall system against uncertainties.

Flexible to design different combinations of reduced-order system with different input and output channels.

INTRODUCTION Deregulation: Restructuring or upgrading of power

system for load requirements.

Power system is generally of large system with time-to-time changing loads.

A control strategy is needed to not only maintains constant frequency and desired tie-line power but also achieve zero steady state error.

Power system main concern is to transport power with quality and optimized performance.

Balances of frequency and voltage should be in preferable limits. If one those falls then entire system will loose stability.

To maintain system stability a control strategy is needed known as Load Frequency Control (LFC).

PROPOSED CONTROL STRATEGY

To obtain the LMI approach we need to know the state space equations for three area power system.

FIGURE-I THREE AREA POWER SYSTEM

Power System state space model :

uDxCyuDxCZuBwBAxx

FIGURE -2 . Three area power system

THREE AREA POWER SYSTEM DYNAMIC MODEL

3f12tieP

23tieP

13tieP

10 –

11 –

12 –

13 –

14 –

15 –

16 –

17 –

18 –

FIGURE 3. Contract Participation Factors (cpf) for contractual loads

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PID control model :

dtdyKdtyKyKu oi

DioiIioiPii Above equation can be written as simply

iii yKu

iy Could be augmented as

dydtyyy oioioii

PID is reduced to SOF (Static Output Feedback) form

uBwBzAz

2322212

Once found original PID gains can be obtained from K

132233

KBCKIK

KBCIKK

ALGORITHM

1. Form state space model of system as in fig 2, then compute matrices of and set performance index γ .

2. Select Q>0 and solve P for the Riccati equation

Set i=1 and Xi=P. 3. Solve the optimization problem for Pi , and ai. Optimization 1: minimize ai subject to the following LMI constraints.

2121 ,,,, CCBBA

0,022 PQPBBPAPPATT

000000

2221211

ICKPBCKDC

CKPBCKDCBP

TPaXBBXXBBPPBBXAPPA 222222

Denoted by the minimized value of *ia ia

4. If the matrix pair (Pi , ) solves the problem. Otherwise go to step 5.

5. Solve the optimization problem for Pi and . Optimization 2: minimize trace (Pi) subject to LMI constraints in step 3 with . Denote by the optimal .

6. If where is prescribed tolerance, go to step 7. otherwise set i=i+1 and Xi=Pi and go to step 3.

7. If obtained solution satisfies gain constant, it is desirable otherwise change constant weights (ni) and γ and go to step 1.

0* ia K

*ii aa *

|||| 1*

11 BPBX

RESULTS

SCENARIO-I : BASE CASE

• This scenario has freedom to have contracts within any of GENCOs in its own area. Each area has equal AGC(Automatic Generation Control) and ACE(Area Control Error) participation factors. Those factors are assuming load variations are taken in corresponding areas-I and III.

• DPM (Dynamic Participation Matrix) helps operator to give load sharing based on the cpf (contract participation factor).

P I DGains 0.008912 0.0012548 0.0002

Obtained PID Gains

L6i6L5i5L4i4L3i3L2i2L1i1Mi ΔPcpfΔPcpfΔPcpfΔPcpfΔPcpfΔPcpfΔP

0.1pu0.1*0.50.1*0.5ΔPM1

0.1puΔPM2

0puΔPM3

0puΔPM4

0.1puΔPM5

0puΔPM6

Similarly

00000000.5000000000.50.500.5000.50.5

FIGURE- 4.Frequency response of area-I

FIGURE- 5. Frequency response of area-II

FIGURE -6. Frequency response of area-III

FIGURE -7. Power generated in Generator-I

FIGURE -8 Power generated in Generator-II

FIGURE-9 Power generated in Generator-III

FIGURE -10Power generated in Generator-IV

FIGURE -11 Power generated in Generator-V

FIGURE -13 Ptie-line error of area 1&2

FIGURE -12 Power generated in Generator-VI

SCENARIO-II : Transaction based on free contracts

This scenario has freedom to have contracts within or without any of GENCOs in the interconnected system. Each area has equal AGC(Automatic Generation Control) and ACE(Area Control Error) participation factors. Those factors are assuming load variations are taken in corresponding all areas-I II and III.

DPM (Dynamic Participation Matrix) helps operator to

give load sharing based on the cpf (contract participation factor).

P I DGains 0.00912 0.00248 0.001

Obtained PID Gains

0.90.7000.250.30.10.10.710.25000.2000.250.2000.300.250.5

L6i6L5i5L4i4L3i3L2i2L1i1Mi ΔPcpfΔPcpfΔPcpfΔPcpfΔPcpfΔPcpfΔP

0.1pu0.1*0.30.1*0.20.1*0.5ΔPM1

0.1puΔPM3

0.1puΔPM2

0.1puΔPM4

0.08puΔPM5

0.1puΔPM6

FIGURE- 16Frequency response of area-I

FIGURE- 17 Frequency response of area-II

FIGURE -19 Power generated in Generator-I

FIGURE- 18Frequency response of area-III

FIGURE -21 Power generated in Generator-III

FIGURE -20 Power generated in Generator-II

FIGURE -22Power generated in Generator-IV

FIGURE -23 Power generated in Generator-V

FIGURE -24 Power generated in Generator-VI

CONCLUSION(S)

The essential objective of this project is to develop robust decentralized controller design approaches for power systems with special importance on problems (i.e. Load Frequency issues) that can be expressed in terms of minimizing a linear objective function under LMI constraints based on control design.

For guaranteed performance and robustness this controller is effective and efficient against variations.

The step by step procedure involves complexity but the achievement through this computation leads to robustness of the entire system.

FUTURE SCOPE

Can be used for any number of area interconnections in power system.

Robustness can be maintained even though the system is complicated.

QUERIES ???