simulation of two area agc system in a competitive environment-07

SIMULATION OF TWO AREA AGC SYSTEM IN ACOMPETITIVE ENVIRONMENT

1. DEREGULATED POWER SYSTEMS

1.1 Introduction

The electricity industry is evolving into a distributed and competitive industry

in which market forces drive the price of electricity and reduce the net cost through

increased competition. Restructuring has necessitated the decomposition of the three

components of electric power industry: generation, transmission and distribution.

Indeed, the separation of transmission ownership from transmission control

is the best application of proforma tariff. An independent operational control of

transmission grid in a restructured industry would facilitate a competitive market for

power generation and direct retail access. However, the independent operation of the

grid cannot be guaranteed without an independent entity such as the independent

system operator (ISO). The ISO is required to be independent of individual market

participants, such as transmission owners, generators, distribution companies and

end-users.

In order to operate the competitive market efficiently while ensuring the

reliability of a power system, the ISO, as the market operator, must establish sound

rules on energy and ancillary services markets, manage the transmission system in a

fair and non-discriminatory fashion, facilitate hedging tools against market risks and

monitor the market to ensure that it is free from market power. The ISO must be

equipped with powerful computational tools, involving market monitoring, ancillary

services auctions and congestion management, for example, in order to fulfill its

responsibility.

Energy and ancillary services were offered as unbundled services and

generating companies (GENCOs) could compete for selling energy to customers by

submitting competitive bids to the electricity market. They could maximize their profits

regardless of the system wide profit.

SRI SAI INSTITUTE OF TECHNOLOGY AND SCIENCE, RAYACHOTI 1


1.2 Market Structure and Operation

1.2.1 Electricity market models

In order to achieve electricity market goals, several models for the market

structure have been considered. Three basic models are outlined as follows:

1.2.1.1 Pool Co Model

A Pool Co is defined as a centralized market place that clears the market for

buyers and sellers. Electric power sellers / buyers submit bids to the pool for the

amounts of power that they are willing to trade in the market. Sellers in a power

market would compete for the right to supply energy to the grid and not for specific

customers. If a market participant bids too high, it may not be able to sell. On the

other hand, buyers compete for buying power and if their bids are too low, they may

not be able to purchase. In this market, low cost generators would essentially be

rewarded.

An ISO within a Pool Co would implement the economic dispatch and

produce a single (spot) price for electricity, giving participants a clear signal for

consumption and investment decisions. The market dynamics in the electricity market

would drive the spot price to a competitive level that is equal to the marginal cost of

most efficient bidders. In this market, winning bidders are paid the spot price that is

equal to the highest bid of the winners.

1.2.1.2 Bilateral Contracts Model

Bilateral contracts are negotiable agreements on delivery and receipt of

power between two traders. These contracts set the terms and conditions of

agreements independent of the ISO. However, in this model the ISO would verify that

a sufficient transmission capacity exists to complete the transactions and maintain the

transmission security. The bilateral contract model is very flexible as trading parties

specify their desired contract terms. However, its disadvantages stem from the high

cost of negotiating and writing contracts, and the risk of the creditworthiness of

counterparties.

1.2.1.3 Hybrid Model



The hybrid model combines various features of the previous two models. In

the hybrid model, the utilization of a Pool Co is not obligatory and any customer would

be allowed to negotiate a power supply agreement directly with suppliers or choose to

accept power at the spot market price. In this model, Pool Co would serve all

participants (buyers and sellers) who choose not to sign bilateral contracts. However,

allowing customers to negotiate power purchase arrangements with suppliers would

offer a true customer choice and an impetus for the creation of a wide variety of

services and pricing options to best meet individual customer needs.

1.2.2 Key Market Entities

The restructuring of electricity has changed the role of traditional entities in a

vertically integrated utility and created new entities that can function independently.

Here, market entities are categorized into market operator (ISO) and market

participants. The ISO is the leading entity in a power market and its functions

determine market rules. The key market entities discussed here include GENCOs and

TRANSCOs. Other market entities include DISCOs, RETAILCOs, aggregators,

brokers, marketers and customers.

1.2.2.1(a) ISO

A competitive electricity market would necessitate an independent

operational control of the grid. The control of the grid cannot be guaranteed without

establishing the ISO. The ISO administers transmission tariffs, maintains the system

security, coordinates maintenance scheduling, and has a role in coordinating long-

term planning.

The ISO should function independent of any market participants, such as

transmission owners, generators, distribution companies and end-users, and should

provide non-discriminatory open access to all transmission system users. The ISO

has the authority to commit and dispatch some or all system resources and to curtail

loads for maintaining the system security (i.e., remove transmission violations,

balance supply and demand and maintain the acceptable system frequency).

Also, the ISO ensures that proper economic signals are sent to all market

participants, which in turn, should encourage efficient use and motivate investment in

resources capable of alleviating constraints.



1.2.2.1(b) GENCOs

A GENCO operates and maintains existing generating plants. GENCOs are

formed once the generation of electric power is segregated from the existing utilities.

A GENCO may own generating plants or interact on behalf of plant owners with the

short-term market (power exchange, power pool, or spot market). GENCOs have the

opportunity to sell electricity to entities with which they have negotiated sales

contracts.

In addition to real power, GENCOs may trade reactive power and operating

reserves. GENCOs are not affiliated with the ISO or TRANSCOs. A GENCO may

offer electric power at several locations that will ultimately be delivered through

TRANSCOs and DISCOs to customers. Its generating assets include power-

producing facilities and power purchase contracts. Since GENCOs are not in a

vertically integrated structure, their prices are not regulated.

In addition, GENCOs cannot discriminate against other market participants

(e.g., DISCOs and RETAILCOs), fix prices, or use bilateral contracts to exercise

market power.

GENCOs may be entitled to funds collected for the stranded power costs

recovery. GENCOs will communicate generating unit outages for maintenance to the

ISO within a certain time (usually declared by the ISO) prior to the start of the outage.

The ISO then informs the GENCOs of all approved outages. In the restructured power

market, the objective of GENCOs is to maximize profits. To do so, GENCOs may

choose to take part in whatever markets (energy and ancillary services markets) and

take whatever actions (arbitraging and gaming). It is a GENCO’s own responsibility to

consider possible risks.

1.2.2.1(c) TRANSCOs



The transmission system is the most crucial element in electricity markets.

The secure and efficient operation of the transmission system is the key to the

efficiency in these markets. A TRANSCO transmits electricity using a high-voltage,

bulk transport system from GENCOs to DISCOs for delivery to customers. It is

composed of an integrated network that is shared by all participants and radial

connections that join generating units and large customers to the network.

The use of TRANSCO assets will be under the control of the regional ISO,

although the ownership continues to be held by original owners in the vertically

integrated structure. TRANSCOs are regulated to provide non-discriminatory

connections and comparable service for cost recovery. A TRANSCO has the role of

building, owning, maintaining and operating the transmission system in a certain

geographical region to provide services for maintaining the overall reliability of the

electrical system.

TRANSCOs provide the wholesale transmission of electricity, offer open

access, and have no common ownership or affiliation with other market participants

(e.g., GENCOs). Authorities at the state and federal levels regulate TRANSCOs, and

they recover their investment and operating costs of transmission facilities using

access charges (which are usually paid by every user within the area / region),

transmission usage charges (based on line flows contributed by each user) and

congestion revenues collected by the ISO.

1.2.2.1(d) DISCOs

A DISCO distributes the electricity, through its facilities, to customers in a

certain geographical region. A DISCO is a regulated (by state regulatory agencies)

electric utility that constructs and maintains distribution wires connecting the

transmission grid to end-use customers. A DISCO is responsible for building and

operating its electric system to maintain a certain degree of reliability and availability.

DISCOs have the responsibility of responding to distribution network outages and

power quality concerns. DISCOs are also responsible for maintenance and voltage

support as well as ancillary services.

2. MODELING OF POWER SYSTEM AND AGC



2.1 Introduction

It is important to realize, that optimized dispatching would be useless without

a method of control over the generator units. Indeed, the control of generator units

was the first problem faced in early power-system design. The methods developed for

control of individual generators and eventually control of large interconnections play a

vital role in modern energy control centers. A generator driven by a steam turbine can

be represented as a large rotating mass with two opposing torques acting on the

rotation. As shown in Figure 2.1, Tmech, the mechanical torque, acts to increase

rotational speed whereas Telec, the electrical torque, acts to slow it down. When Tmech

and Telec are equal in magnitude, the rotational speed, ω, will be constant. If the

electrical load is increased so that Telec is larger than Tmech, the entire rotating system

will begin to slow down.

Since it would be damaging to let the equipment slow down too far,

something must be done to increase the mechanical torque Tmech to restore

equilibrium; that is, to bring the rotational speed back to an acceptable value and the

torques to equality so that the speed is again held constant. This process must be

repeated constantly on a power system because the loads change constantly.

Furthermore, because there are many generators supplying power into the

transmission system, some means must be provided to allocate the load changes to

the generators. To accomplish this, a series of control systems are connected to the

generator units. A governor on each unit maintains its speed while supplementary

control, usually originating at a remote control center, acts to allocate generation

Fig. 2.1 Mechanical and electrical torques in a generating unit.

2.2 Generator model



Before starting, it will be useful for us to define our terms,

=Phase angle of a rotating machine (rad)

=rotational speed (rad / sec)

=Net accelerating torque in machine ( or or )

= Mechanical torque exerted on the machine by the turbine

= Electrical torque exerted on the machine by the generator

=Net accelerating power ( )

= Mechanical power input

= Electrical power output

= Moment of inertia for the machine ( or )

= Angular momentum of the machine ( )

The relationship between phase angle deviation, speed deviation, and net

accelerating torque is,

Using the relationship between rotational phase angle deviation and rotational speed,

we can rewrite the above equation as,

Considering the net torque as the sum of the steady state value and the deviation

term,

Where,



Then,

Similarly for power also we can write,

From the above equations we can see that,

Assume that the steady state quantities can be neglected since,

And also assume that second order terms involving deviation terms can be neglected.

Then,

From the expression, we can write that,

Since , we can write the above equation as,

In Laplace domain the above expression can be represented as,



Since, motor loads are dominant in electrical load, it is necessary to model

the effect of change in frequency on the net load drawn by the system.

The relationship between the changes in load due to the change in frequency is given

by,

And also we can write,

Power balance equation without any interconnection can be written as,

2.3 Load model

The loads on a power system consist of a variety of electrical devices. Some

of them are purely resistive, some are motor loads with variable power frequency

characteristics and others exhibit quite different characteristics. Since motor loads are

a dominant part of the electrical load, there is a need to model the effect of a change

in frequency on the net load drawn by the system. The relationship between the

changes in load due to the change in frequency is given by,

∆PL(freq) = D∆ωWhere,

D - Percent change in load divided by percent change in frequency.

.

Fig. 2.2 Generator-load model



2.4 Prime mover model

The prime mover driving a generator unit may be a steam turbine or a hydro

turbine. The models for the prime mover must take account of the steam supply and

boiler control system characteristics in the case of a steam turbine, or the penstock

characteristics for a hydro turbine throughout the remainder of this chapter, only the

simplest prime-mover model, the non reheat turbine, will be used. The model for a

non reheat turbine, shown in Figure 2.3 relates the position of the valve that controls

emission of steam into the turbine to the power output of the turbine,

Where,

TCH = "charging time" time constant

PValve = per unit change in valve position from nominal

Fig. 2.3 Prime mover model

The combined prime-mover-generator-load model for a single generating unit can be

built by combining Figure 2.2 and 2.3, as shown in Figure 2.4



Fig. 2.4 Combined prime-mover-generator-load model

2.5 Governor model

Suppose a generating unit is operated with fixed mechanical power output

from the turbine. The result of any load change would be a speed change sufficient to

cause the frequency-sensitive load to exactly compensate for the load change. This

condition would allow system frequency to drift far outside acceptable limits.

This is overcome by adding a governing mechanism that senses the

machine speed and adjusts the input valve to change the mechanical power output to

compensate for load changes and to restore frequency to nominal value. The earliest

such mechanism used rotating “fly balls” to sense speed and to provide mechanical

motion in response to speed changes.

Modern governors use electronic means to sense speed changes and often

use a combination of electronic, mechanical and hydraulic means to effect the

required valve position changes. The simplest governor, called the isochronous

governor, adjusts the input valve to a point that brings frequency back to nominal

value. If we simply connect the output of the speed-sensing mechanism to the valve

through a direct linkage, it would never bring the frequency to nominal.

To force the frequency error to zero, one must provide what control

engineers call reset action. Reset action is accomplished by integrating the frequency

(or speed) error, which is the difference between actual speed and desired or

reference speed.

We will illustrate such a speed-governing mechanism with the diagram

shown in Figure 2.5.The speed-measurement device’s output, 𝜔o, is compared with a

reference, ωref, to produce an error signal, ∆ω. The error, ∆ω, is negated and then

amplified by a gain KG and integrated to produce a control signal, ∆Pvalve, which

causes the main steam supply valve to open (∆Pvalve position) when ∆ω is negative.

If, for example, the machine is running at reference speed and the electrical load

increases, 𝜔 will fall below ωref and ∆ω will be negative. The action of the gain and

integrator will be to open the steam valve, causing the turbine to increase its



mechanical output, thereby increasing the electrical output of the generator and

increasing the speed ωo. When ωo exactly equals the steam valve stays at the new

position (further opened) to allow the turbine generator to meet the increased

electrical load.

Fig. 2.5 Isochronous governor

The isochronous (constant speed) governor of Figure 2.5 cannot be used if

two or more generators are electrically connected to the same system since each

generator would have to have precisely the same speed setting or they would “fight”

each other, each trying to pull the system’s speed (or frequency) to its own setting. To

be able to run two or more generating units in parallel on a generating system, the

governors are provided with a feedback signal that causes the speed error to go to

zero at different values of generator output. This can be accomplished by adding a

feedback loop around the integrator as shown in Figure 2.6. The block diagram for

this governor with droop is shown in Figure 2.7, where the governor now has a net

gain of 1/R and a time constant TG.

The result of adding the feedback loop with gain R is a governor

characteristic as shown in Fig. 2.8. The value of R determines the slope of the

characteristic. That is, R determines the change on the unit’s output for a given

change in frequency. Common practice is to set R on each generating unit so that a

change from 0 to 100% (i.e., rated) output will result in the same frequency change for



each unit. As a result, a change in electrical load on a system will be compensated by

generator unit output changes proportional to each unit’s rated output.

Fig. 2.6 Governor with speed-droop feedback loop

If two generators with drooping governor characteristics are connected to a

power system, there will always be a unique frequency, at which they will share a load

change between them. This is illustrated in Figure 2.9 showing two units with

drooping characteristics connected to a common load.



Fig. 2.7 Block diagram of governor with droop

Fig. 2.8 Speed-droop characteristic.



Fig. 2.9 Allocation of unit outputs with governor droop

As shown in Figure 2.9, the two units start at a nominal frequency of fo When

a load increase, ΔPL causes the units to slow down, the governors increase output

until the units seek a new, common operating frequency ‘f ‘. The amount of load

pickup on each unit is proportional to the slope of its droop characteristic. Unit 1

increases its output from P1 to P’1. Unit 2 increases its output from P2 to P’2 such

that the net generation increase, P’1 - P1+ P’2- P2, is equal to ΔPL. Note that the actual

frequency sought also depends on the load’s frequency characteristic as well.

Figure 2.6 shows an input labeled “load reference set point.” By changing

the load reference, the generator’s governor characteristic can be set to give

reference frequency at any desired unit output. This is illustrated in Figure 2.10.The

basic control input to a generating unit as far as generation control is concerned is the

load reference set point. By adjusting this set point on each unit, a desired unit

dispatch can be maintained while holding system frequency close to the desired

nominal value.



Fig. 2.10 Speed-changer settings

Note that a steady-state change in ΔPvalve, of 1.0 pu requires a value of R pu

change in frequency, Δω .One often hears unit regulation referred to in percent. For

instance, a 3% regulation for a unit would indicate that a 100 % (1.0 pu) change in

valve position (or equivalently a 100% change in unit output) requires a 3% change in

frequency. Therefore, R is equal to pu change in frequency divided by pu change in

unit output. That is,

At this point, we can construct a block diagram of a governor-prime-mover

rotating mass / load model as shown in Figure 2.11 Suppose that this generator

experiences a step increase in load,



Fig. 2.11 Block diagram of governor, prime mover and rotating mass.

2.6 Tie line power calculation

The power flowing across a transmission line can be modeled using the DC

load flow method shown:

This tie flow is a steady-state quantity. For purposes of analysis here, we will

perturb the above equation to obtain deviations from nominal flow as a function of

deviations in phase angle from nominal.



Note that Δ must be in radians for ΔPtie to be in pu MW, but Δω is in per

unit speed change. Therefore, we must multiply Δω by 377 rad/sec (the base

frequency in rad/sec at 60 Hz). T may be thought of as the “tie-line stiffness”

coefficient.

Suppose now that we have an interconnected power system broken into two

areas each having one generator. The areas are connected by a single transmission

line. The power flow over the transmission line will appear as a positive load to one

area and an equal but negative load to the other, or vice versa, depending on the

direction of flow. The direction of flow will be dictated by the relative phase angle

between the areas, which is determined by the relative speed deviations in the areas.

A block diagram representing this interconnection can be drawn as in Figure 2.12.

Note that the tie power flow was defined as going from area 1 to area 2; therefore, the

flow appears as a load to area 1 and a power source (negative load) to area 2. If one

assumes that mechanical powers are constant, the rotating masses and tie line

exhibit damped oscillatory characteristics known as synchronizing oscillations.



Fig. 2.12 Block diagram of inter connected areas

2.7 Generation control

Automatic generation control (AGC) is the name given to a control system

having three major objectives:

1. To hold system frequency at or very close to a specified nominal value.

2. To maintain the correct value of interchange power between control.

3. To maintain each unit's generation at the most economic value.

2.7.1 Supplementary Control Action

To understand each of the three objectives just listed, we may start out

assuming that we are studying a single generating unit supplying load to an isolated

power system. As shown in Section 2.4, a load change will produce a frequency

change with a magnitude that depends on the droop characteristics of the governor

and the frequency characteristics of the system load. Once a load change has

occurred, a supplementary control must act to restore the frequency to nominal value.

This can be accomplished by adding a reset (integral) control to the governor, as



shown in Figure 2.13. The reset control action of the supplementary control will force

the frequency error to zero by adjustment of the speed reference set point.

Fig. 2.13 Supplementary control added to generating unit

2.7.2 Tie-Line Control

When two utilities interconnect their systems, they do so for several

reasons. One is to be able to buy and sell power with neighboring systems whose

operating costs make such transactions profitable. Further, even if no power is being

transmitted over ties to neighboring systems, if one system has a sudden loss of a

generating unit, the units throughout all the interconnection will experience a

frequency change and can help in restoring frequency. The system frequency and the

net power flowing in or out over the tie lines. Such a control scheme would, of

necessity, have to recognize the following:

1. If frequency decreased and net interchange power leaving the system

2. If frequency decreased and net interchange power leaving the system

increased, a load increase has occurred outside the system decreased, a load

increase has occurred inside the system.

.



Fig. 2.14 Tie-line bias supplementary control for two areas

2.7.3 Generation Allocation

If each control area in an interconnected system had a single generating

unit, the control system of Figure 2.14 would suffice to provide stable frequency and

tie-line interchange. However, power systems consist of control areas with many

generating units with outputs that must be set according to economics. That is, we

must couple an economic dispatch calculation to the control mechanism so it will

know how much of each area’s total generation is required from each individual unit.

One must remember that a particular total generation value will not usually exist for a

very long time, since the load on a power system varies continually as people and

industries use individual electric loads.



Therefore, it is impossible to simply specify a total generation, calculate the

economic dispatch for each unit and then give the control mechanism the values of

MW output for each unit unless such a calculation can be made very quickly. Until the

widespread use of digital computer-based control systems, it was common practice to

construct control mechanisms such as we have been describing using analog

computers. Although analog computers are not generally proposed for new control-

center installations today, there are some in active use. An analog an area on an

instantaneous basis through the use of function generators set to equal the units’

incremental heat rate curves. B matrix loss formulas were also incorporated into

analog schemes by setting the matrix coefficients on precision potentiometers.

When using digital computers, it is desirable to be able to carry out the

economic-dispatch calculations at intervals of one to several minutes. Either the

output of the economic dispatch calculation is fed to an analog computer (i.e., a

“digitally directed analog” control system) or the output is fed to another program in

the computer that executes the control functions (i.e., a “direct digital” control system).

Whether the control is analog or digital, the allocation of generation must be made

instantly when the required area total generation changes. Since the economic-

dispatch calculation is to be executed every few minutes, a means must be provided

to indicate how the generation is to be allocated for values of total generation other

than that used in the economic dispatch calculation.

The allocation of individual generator output over a range of total generation

values is accomplished using base points and participation factors. The economic-

dispatch calculation is executed with a total generation equal to the sum of the

present values of unit generation as measured. The result of this calculation is a set

of base-point generations, Pi base which is equal to the most economic output for each

generator unit. The rate of change of each unit’s output with respect to a change in

total generation is called the unit’s participation factor, pf. The base point and

participation factors are used as follows,



Note that by definition, the participation factors must sum to unity.

3. STATE FEEDBCK AND REDUCED ORDER

BASED CONTROLLERS

3.1 Introduction

In optimal control one attempt to find a controller that provides the best

possible performance with respect to some given measure of performance. For

example, the controller that uses the least amount of control-signal energy to take the



output to zero. In this case the measure of performance (also called the optimality

criterion) would be the control signal energy. In general, optimality with respect to

some criterion is not the only desirable property for a controller. One would also like

stability of the closed-loop system, good gain and phase margins, robustness with

respect to unmodeled dynamics, etc.

In this chapter, we study controllers that are optimal with respect to energy-

like criteria. These are particularly interesting because the minimization procedure

automatically produces controllers that are stable and somewhat robust. In fact, the

controllers obtained through this procedure are generally so good that we often use

them even when we do not necessarily care about optimizing for energy. Moreover,

this procedure is applicable to multiple-input / multiple-output processes for which

classical designs are difficult to apply.

3.2 State Observers

In the pole-placement approach to the design of control systems, we

assumed that all state variables are available for feedback. In practice, however, not

all state variables are available for feedback. Then we need to estimate unavailable

state variables. Estimation of un-measurable state variables is commonly called

observation. A device (or a computer program) that estimates or observes the state

variables is called a state observer, or simply an observer. If the state observer

observes all state variables of the system, regardless of whether some state variables

are available for direct measurement, it is called a full-order state observer. There are

times when this will not be necessary, when we will need observation of only the un-

measurable state variables, but not of those that are directly measurable as well.

For example, since the output variables are observable and they are linearly related

to the state variables, we need not observe all state variables, but observe only n - m

state variables, where n is the dimension of the state vector and m is the dimension of

the output vector. An observer that estimates fewer than n state variables, where n is

the dimension of the state vector, is called a reduced-order state observer or, simply,

a reduced-order observer. If the order of the reduced-order state observer is the

minimum possible, the observer is called a minimum-order state observer or



minimum-order observer. In this chapter, we shall discuss both the full-order state

observer and the minimum-order state observer.

3.2.1 State Observer

A state observer estimates the state variables based on the measurements

of the output and control variables. Here the concept of observability plays an

important role. As we shall see later, state observers can be designed if and only if

the observability condition is satisfied. In many practical cases, the observed state

vector is used in the state feedback to generate the desired control vector.

Consider the plant defined by,

The observer is a subsystem to reconstruct the state vector of the plant. The

mathematical model of the observer is basically the same as that of the plant, except

that we include an additional term that includes the estimation error to compensate for

inaccuracies in matrices A and B and the lack of the initial error. The estimation error

or observation error is the difference between the measured output and the estimated

output. The initial error is the difference between the initial state and the initial

estimated state. Thus, we define the mathematical model of the observer to be,

Where,

- The estimated state and

C - The estimated output.

The inputs to the observer are the output y and the control input u. Matrix

Ke, which is called the observer gain matrix, is a weighting matrix to the correction

term involving the difference between the measured output y and the estimated


1

2

3


output C . This term continuously corrects the model output and improves the

performance of the observer. Figure below shows the block diagram of the system

and the full-order state observer.

Fig. 3.1 Full-order state observer

3.2.1(a) Full-Order State Observer

The order of the state observer that will be discussed here is the same as

that of the plant. Assume that the plant is defined by Equations (1) and (2) and the

observer model is defined by Equation (3).

To obtain the observer error equation, let us subtract Equation (3) from Equation (1):

We define the error vector e as,

From Equation (4), we see that the dynamic behavior of the error vector is

determined by the eigen values of matrix A – KeC. If matrix A – KeC is a stable matrix,


4


the error vector will converge to zero for any initial error vector e (0). That is will

converge to x (t) regardless of the values of x (0) and . If the eigen values of

matrix A – KeC are chosen in such a way that the dynamic behavior of the error

vector is asymptotically stable and is adequately fast, then any error vector will tend to

zero (the origin) with an adequate speed.

If the plant is completely observable, then it can be proved that it is possible

to choose matrix Ke such that A – KeC has arbitrarily desired eigen values. That is,

the observer gain matrix Ke can be determined to yield the desired matrix A – KeC.

Reduced-Order Observer, The observers discussed thus far are designed to

reconstruct all the state variables. In practice, some of the state variables may be

accurately measured. Such accurately measurable state variables need not be

estimated. Suppose that the state vector x is an n-vector and the output vector y is an

m-vector that can be measured. Since m output variables are linear combinations of

the state variables, m state variables need not be estimated. We need to estimate

only n – m state variables. Then the reduced-order observer becomes an (n - m) th

order observer. Such an (n - m) th-order observer is the minimum-order observer.



Fig. 3.2 Observed-state feedback control system with a minimum-order observer

It is important to note, however, that if the measurement of output variables

involves significant noises and is relatively inaccurate, then the use of the full-order

observer may result in a better system performance. To present the basic idea of the

minimum-order observer, we suppose that only some of the state variables are

measurable. These are defined as output variables such as,

The interesting case is when have less sensors available than the number of states

(n), p < n.

Suppose we can measure some of the state variables contained in x, and the state

vector x is partitioned into two sets,

And the observation equation is,



Where,

C1 - square and non singular matrix.

The full order observer for the states is then,

But we do not need to solve first observer equation for x1 because these states can

be solved directly using,

In this case the observer for those states that cannot be measured directly is

designed as follows,

This is a dynamic system of the same order as the number of state variables

that cannot be measured directly. The dynamic behavior of this reduced order

observer is governed by the eigen values of A12, a matrix over which the designer has

no control. Since there is no assurance that the eigen values of A22 are suitable, we

need more general system for the reconstruction of x2. We take,

Where,

Define the estimation error as follows,



And we get,

Since,

We get,

In order for the error to be independent of x1, x2, and u, the matrices multiplying x1, x2,

and u must vanish:

F = A22 - LC1A12

H = B2 - LC1 B1

Then,

and the stability of the observer dynamic system. The eigen values of F must lie in

the left hand-side of s-plane. Therefore, we see that the problem of reduced order

observer is similar to the full order observer with ( playing the role of

.



Fig. 3.3 Block diagram of reduced order observer

3.3 Linear Quadratic Regulation (LQR)

3.3.1 Model Development and Analysis

First, we will develop a state space model for the flexible joint that will be

used in the LQR and observer designs. For this we should refer to the model

development section on the flexible link that is in the design challenges document that

is on the web. Suppose that the state space model,

has an n × 1 state x and a 1 × 1 input u. Find the A, B and C matrices for a state

space description of the plant.



3.3.2 LQR Development

Suppose that we have sensors to measure the entire state and that we use

a controller (regulator),

that seeks to drive the state to zero. Regulator design entails finding the n × 1 gain

vector K. We could use pole placement via Ackerman’s formula. Here, we use the

LQR methodology to specify the gain K. For this, let

and we seek to find the gain vector K to minimize this “cost function”. Minimization of

J results in moving x to zero with as little control energy and state deviations as

possible, with the balance between control energy and state deviations specified via

the Q and R matrices. Here, assume the Q matrix of order n×n is diagonal with

diagonal elements qi ≥ 0 (each providing a weight for a different element of the

deviation of the state) and the scalar R > 0. The values for Q and R are used as

design parameters. How to tune them? If we choose all the qi = 0 this represents that

we do not care what type of excursions the state has while the control tries to force

the state to zero. High values of qi relative to R mean that we are willing to use lots of

control energy to keep state excursions small while driving it to zero. Clearly, we

cannot pick R = 0 as this results in allowing infinite control energy to force the state to

zero, typically then very fast. Finding the K to minimize J involves solving a “Ricatti

equation.”



4. RESTRUCTURED POWER SYSTEM FOR AGC

WITH TWO AREAS

4.1 Traditional Vs Restructured power systems

In a traditional power system structure, the generation, transmission and

distribution are owned by a single entity called a Vertically Integrated Utility (VIU),

which supplies power to the customers at regulated rates. Such VIU’s are

interconnected by tie lines. Following a load disturbance within an area, the frequency

of system experiences a transient change and the feedback mechanism comes into

play and generates an appropriate rise / lower signal to the turbine to make the

generation follow the load. In steady state, the generation is matched with the load,

driving the tie line power and frequency deviations to zero.

In the restructured (deregulated) power systems, the VIU no longer exists.

However, the common objectives, i.e. restoring the frequency and the net interchanges

to their desired values for each control area remain. In the vertically integrated power

system structure, it is assumed that some generator units are equipped with secondary

control and frequency regulation requirements, but in an open energy market, even

such generators / GENCOs may or may not participate in the AGC.

Generators / GENCOs are selected through bidding for AGC in deregulated

power system. Therefore, in a control area with an open access policy, there comes

the need for novel model and efficient control strategies to maintain reliability and

eliminate the frequency error. In recent years several proposed AGC scenarios have

attempted to adapt traditional AGC schemes to the change of environment in the

power system after deregulation. Some of these studies try to modify the conventional

AGC system to take into account the effect of bilateral contracts on the dynamics or try

to improve the dynamical transient response of system under deregulation

environment. We designed reduced order observer based controller for the

deregulated AGC to estimate the unmeasurablre states.



4.2 Restructured Power system for AGC with two areas

In the competitive environment of power system, the vertically integrated

utility no longer exists. Deregulated power system consists of generating companies

(GENCOs), distribution companies (DISCOs), transmission companies (TRANSCOs)

and independent system operator (ISO). However, the common AGC goals, i.e.,

restoring the frequency and the net interchanges to their desired values for each

control area, still remain. The power system is assumed to contain two areas and

each area includes two GENCOs and also two DISCOs as shown in fig. 4.1. and the

block diagram of the generalized LFC scheme for two area deregulated power system

is shown in fig. 4.2. A DISCO can contract individually with any GENCO for power

and these transactions are made under the supervision of ISO.

To make the visualization of these contracts easier, the concept of a “DISCO

participation matrix (DPM)” will be used. Essentially, DPM gives the participation of a

DISCO in contract with a GENCO.

Fig.4.1 configuration of the deregulated power system

In DPM, the number of rows has to be equal to the number of GENCOs and

the number of columns has to be equal to the number of DISCOs in the system. Any

entry of this matrix is a fraction of total load power contracted by a DISCO toward a

GENCO.

As a result, total of entries of column belong to DISCO i of DPM is ∑ i cpf ij =1.



The corresponding DPM to the considered power system having two areas

and each of them including two DISCOs and GENCOs is given as follows,

Where, cpf represents “contract participation factor” and is like signals that

carry information as to which GENCO has to follow load demanded by which DISCO.

The actual and scheduled steady state power flows on the tie line are given as,



And at any given time, the tie line power error ∆Ptie1-2, error is defined as,

This error signal is used to generate the respective ACE signal as in the

traditional scenario.

ACE1 = B1∆f1 + ∆Ptie1-2, error

ACE2 = B2∆f2 + ∆Ptie2-1, error

Fig. 4.2 Modified LFC system in a deregulated environment



The dotted and dashed lines in fig.4.2 show the demand signals based on

the possible contracts between GENCOs and DISCOs that carry information as to

which GENCO has to follow a load demanded by that DISCO. These new information

signals were absent in the traditional LFC scheme. As there are many GENCOs in

each area, the ACE signal has to be distributed among them due to their ACE

participation factor in LFC.

4.3 Controller Design

4.3.1 State space model

The system in fig4.2 is characterized in state space as:

Where,

x is the state vector and u is the vector of power demands of the DISCOs.

u = [∆PL1 ∆PL2 ∆PL3 ∆PL4] T

x = [∆ω1 ∆ω2 ∆PG1 ∆PG2 ∆PG3 ∆PG4 ∆Ptie1-2, actual ∆Pm1∆Pm2 ∆Pm3 ∆Pm4 ∫ACE1 ∫ACE2] T

Then the state space model of given system given as:

Fig. 4.3 State space model of given system

4.3.2 Full State feed beck model

Here, we assumed that all the state variables are available for feedback.

The control signal is,



u= -kx

Where,

k is controller gain matrix.

Then,

We have to design matrix ‘k’ such that the eigen values of (A-Bk) lie on left half of the

s - plane.

Fig. 4.4 Two area AGC model with full state feedback control

4.3.3 Reduced Order Observer model

For the system defined by the equations,

Feed back control law is,

u = -kx

We suppose that only some of the state variables are measurable. These

are defined as output variables such as:

The interesting case is when have less sensors available than the number of states

(n), p < n.

Suppose we can measure some of the state variables contained in x, and the state

vector x is partitioned into two sets,

X1 = variables that can be measured directly.



X2 = variables that cannot be measured directly.

Where,

x1 = [∆ω1 ∆ω2 ∆PG1 ∆PG2 ∆PG3 ∆PG4 ∆Ptie1-2, actual] T

x2 = [∆Pm1 ∆Pm2 ∆Pm3 ∆Pm4 ∫ACE1 ∫ACE2] T

And the observation equation is,

Where,

C1 - Square and non singular matrix.

The full order observer for the states is then,

But we do not need to solve first observer equation for x1 because these states can

be solved directly using,

In this case the observer for those states that cannot be measured directly is

designed as follows,

This is a dynamic system of the same order as the number of state variables

that cannot be measured directly. The dynamic behavior of this reduced order

observer is governed by the eigen values of A12, a matrix over which the designer has

no control. Since there is no assurance that the eigen values of A22 are suitable, we

need more general system for the reconstruction of x2. We take,



Where,

We define the estimation error as follows,

And we get,

Since,

We get,

In order for the error to be independent of x1, x2, and u, the matrices multiplying x1,

x2 and u must vanish,

F = A22 - LC1A12

H = B2 - LC1 B1

Then,

and the stability of the observer dynamic system. The eigen values of F must lie in the

left hand-side of s plane. Therefore, we see that the problem of reduced order



observer is similar to the full order observer with ( playing the role of

.

Fig. 4.5 Block diagram of reduced order observer controller



5. SIMULATION RESULTS

In this chapter, to illustrate the performance of the reduced order observer

controller against load variations, simulations are performed for one scenario of

possible contracts under various operating conditions and large load demands and it

is assumed that all of the changes in load demands occur in bilateral contract and

there is no any violation of contracted demands.

5.1 Scenario: Transaction based on free contracts

In this scenario the performance of the reduced order observer controller is

compared with full state feedback controller. The simulations are done using MATLAB

/ SIMULINK.The power system parameters are given in tables below,

5.1 (a) GENCOs parameters

Table 5.1 (a) GENCOs parameters



5.1 (b) Control area parameters

Table 5.1 (b) Control area parameters

In this scenario, DISCOs have freedom to have a contract with any GENCO

in their or other areas. So all the DISCOs contract with the GENCOs for power based

on following DPM,

Based on this DPM, GENCO2 doesn’t have any contract with other DISCOs.

The off diagonal blocks of the DPM correspond to the contract of a DISCO in one

area with a GENCO in another area. It is assumed that each DISCO demands 0.1pu

MW power from GENCOs as defined in DPM and each GENCO participated in AGC

as defined by following apf,

apf1=0.75, apf2=0.25, apf3=0.5, apf4=0.5.

For the DPM mentioned above, GENCOs generation must be

∆PG1 = 0.5 (0.1) + 0.25 (0.1) + o + 0.3 (0.1) = 0.105 puMW

∆PG2 = 0.0 puMW

∆PG3 = 0.22 puMW

∆PG4 = 0.075 puMW

5.2 MATLAB code

Here, code is written to give inputs separately to the corresponding blocks of

simulink diagrams as it is complex to give the inputs directly.



%%%%%%System Parameters....................

T12 = 0.245;

Tg1 = 0.06;

Tt1 = 0.32;

R1=2.4;

Tg2 = 0.08;

Tt2 = 0.3;

R2=2.5;

Kp1 = 102;

Tp1 = 20;

B1 = 0.425;

K1 = .8;

Tg3 = 0.06;

Tt3 = 0.03;

R3=2.5;

Tg4 = 0.07;

Tt4 = 0.32;

R4=2.7;

Kp2 = 102;

Tp2 = 25;

B2 = 0.396;

K2= .8;

apf1 = 0.75;

apf2 = 0.25;

apf3 = 0.5;

apf4 = 0.5;

cpf = [0.5 0.25 0 0.3;

0 0 0 0;

0 0.5 1 0.7;

0.5 0.25 0 0];

%%%Defining State Space model Matrices..........

A11 = [-1 / Tp1 0 Kp1 / Tp1 Kp1 / Tp1 0 0 -Kp1 / Tp1;



0 -1 / Tp2 0 0 Kp2 / Tp2 Kp2 / Tp2 Kp2 / Tp2

0 0 -1 / Tt1 0 0 0 0;

0 0 0 -1 / Tt2 0 0 0;

0 0 0 0 -1 / Tt3 0 0;

0 0 0 0 0 -1 / Tt4 0;

T12 / (2*pi) -T12 / (2*pi) 0 0 0 0 0];

A12 = [0 0 0 0 0 0;

0 0 0 0 0 0;

1 / Tt1 0 0 0 0 0;

0 1 / Tt2 0 0 0 0;

0 0 1 / Tt3 0 0 0;

0 0 0 1 / Tt4 0 0;

0 0 0 0 0 0];

A21 = [-1 / (R1*Tg1*2*pi) 0 0 0 0 0 0;

-1 / (R2*Tg2*2*pi) 0 0 0 0 0 0

0 -1 / (R3*Tg3*2*pi) 0 0 0 0 0;

0 -1 / (R4*Tg4*2*pi) 0 0 0 0 0;

B1 / (2*pi) 0 0 0 0 0 1;

0 B2 / (2*pi) 0 0 0 0 -1];

A22 = [-1 / Tg1 0 0 0 (-K1*apf1) / Tg1 0;

0 -1 / Tg2 0 0 (-K1*apf2) / Tg2 0;

0 0 -1 / Tg3 0 0 (-K1*apf3) / Tg3;

0 0 0 -1 / Tg4 0 (-K1*apf4) / Tg4;

0 0 0 0 0 0;

0 0 0 0 0 0];

Ba = [-Kp1 / Tp1 -Kp1 / Tp1 0 0;

0 0 -Kp2/Tp2 -Kp2 / Tp2;

0 0 0 0;

0 0 0 0;

0 0 0 0;

0 0 0 0;

0 0 0 0];



Bb = [cpf (1,1) / Tg1 cpf (1,2) / Tg1 cpf (1,3) / Tg1 cpf (1,4) / Tg1;

cpf (2,1) / Tg2 cpf (2,2) / Tg2 cpf (2,3) / Tg2 cpf (2,4) / Tg2;

cpf(3,1) / Tg3 cpf (3,2) / Tg3 cpf (3,3) / Tg3 cpf(3,4) / Tg3;


cpf (3,1) + cpf (4,1) cpf (3,2) + cpf (4,2) - (cpf (1,3) + cpf (2,3)) -

(cpf (1,4) + cpf (2,4));

-(cpf (3,1) + cpf (4,1)) - (cpf (3,2) + cpf (4,2)) cpf (1,3) + cpf (2,3)

cpf (1,4) + cpf (2,4)];

C1 = eye (7, 7);

Q1 = eye (6, 6);

Ra = eye (7,7);

[Ke, Se, Ee] = lqr (A22', A12', Q1, 100*Ra);

L = Ke';

%%%%%Weightage for the State Parameters for control action.......

C = [1 0 0 0 0 0 0 0 0 0 0 0 0;

0 1 0 0 0 0 0 0 0 0 0 0 0;

0 0 1 0 0 0 0 0 0 0 0 0 0;

0 0 0 1 0 0 0 0 0 0 0 0 0;

0 0 0 0 1 0 0 0 0 0 0 0 0;

0 0 0 0 0 1 0 0 0 0 0 0 0;

0 0 0 0 0 0 1 0 0 0 0 0 0];

D = [0];

Q = [(T12*T12) + 1 - (T12^2) 0 0 0 0 0 0 0 0 0 0 0;

-(T12^2) (T12*T12) + 1 0 0 0 0 0 0 0 0 0 0 0;

0 0 0 0 0 0 0 0 0 0 0 0 0;

0 0 0 0 0 0 0 0 0 0 0 0 0;

0 0 0 0 0 0 0 0 0 0 0 0 0;

0 0 0 0 0 0 0 0 0 0 0 0 0;

0 0 0 0 0 0 1 0 0 0 0 0 0;

0 0 0 0 0 0 0 0 0 0 0 0 0;

0 0 0 0 0 0 0 0 0 0 0 0 0;

0 0 0 0 0 0 0 0 0 0 0 0 0;



0 0 0 0 0 0 0 0 0 0 0 0 0;

0 0 0 0 0 0 0 0 0 0 0 1 0;

0 0 0 0 0 0 0 0 0 0 0 0 1];

%%%%%Weightage for the Input Parameters for control action.......

R = eye (4);

delPd = [0.1;0.1;0.1;0.1];

A = [-1 / Tp1 0 Kp1 / Tp1 Kp1 / Tp1 0 0 -Kp1 / Tp1 0 0 0 0 0 0;

0 -1 / Tp2 0 0 Kp2 / Tp2 Kp2 / Tp2 Kp2 / Tp2 0 0 0 0 0 0;

0 0 -1 / Tt1 0 0 0 0 1 / Tt1 0 0 0 0 0;

0 0 0 -1 / Tt2 0 0 0 0 1 / Tt2 0 0 0 0;

0 0 0 0 -1 / Tt3 0 0 0 0 1 / Tt3 0 0 0;

0 0 0 0 0 -1 / Tt4 0 0 0 0 1 / Tt4 0 0;

T12 / (2*pi) - T12 / (2*pi) 0 0 0 0 0 0 0 0 0 0 0;

-1 / (R1*Tg1*2*pi) 0 0 0 0 0 0 -1 / Tg1 0 0 0 (-K1*apf1) / Tg1 0;

-1 / (R2*Tg2*2*pi) 0 0 0 0 0 0 0 -1 / Tg2 0 0 (-K1*apf2) / Tg2 0;

0 -1 / (R3*Tg3*2*pi) 0 0 0 0 0 0 0 -1 / Tg3 0 0 (-K2*apf3) / Tg3;

0 -1 / (R4*Tg4*2*pi) 0 0 0 0 0 0 0 0 -1 / Tg4 0 (-K2*apf4) / Tg4;

B1 / (2*pi) 0 0 0 0 0 1 0 0 0 0 0 0;

0 B2/(2*pi) 0 0 0 0 -1 0 0 0 0 0 0];

B = [-Kp1/Tp1 -Kp1/Tp1 0 0;

0 0 -Kp2/Tp2 -Kp2/Tp2;

0 0 0 0;

0 0 0 0;

0 0 0 0;

0 0 0 0;

0 0 0 0;





cpf (3,1) + cpf (4,1) cpf (3,2) + cpf (4,2) - (cpf (1,3) + cpf (2,3)) –

(cpf (1,4) + cpf (2,4));



-(cpf(3,1)+ cpf (4,1)) - (cpf (3,2) + cpf (4,2)) cpf (1,3) + cpf (2,3)

cpf (1,4) + cpf (2,4)];

[K,S,E] = lqr(A,B,Q,100*R);

5.3 SIMULINK diagrams

5.3.1 SIMULINK diagram of AGC model without controller



Fig. 5.1 Simulink diagram of AGC model without controller

5.3.2 SIMULINK diagram of AGC model with full state feedback

controller



Fig. 5.2 Simulink diagram of AGC model with full state feedback controller

5.3.3 SIMULINK diagram of AGC model with reduced order observer

controller



Fig. 5.3 Simulink diagram of AGC model with reduced order observer controller

After running the code only the simulink diagrams are to be run to view the

out put waveforms.

5.4 Output waveforms



Fig. 5.4 Change in frequency of area 1

Fig. 5.5 Change in frequency of area 2



Fig. 5.6 Change in generation of GENCO 1




Fig. 5.10 Change in tie-line power

Fig. 5.11 Change in governor output of GENCO 1



Fig. 5.15 Response of integral area control error for area 1

Fig. 5.16 Response of integral area control error for area 2



In the above waveforms, response plotted in blue color constitutes the

response without controller, in green color corresponds to response of reduced order

observer based controller and in red color corresponds to the response of full state

feedback controller

Here, by observing the waveforms we can say that the reduced order

observer does not show any effect on the response of measurable outputs and its

response is same as that of full state feedback controller in case of measurable

outputs.

But, for unmeasured outputs the response with full state feedback is heavily

deviating from what the actual response is. Now, here in the case of unmeasured

outputs the reduced order observer estimates them and gives it to feedback and

reduces the peak deviations of frequencies, tie-line power and inadvertent

interchanges.

By this, it can be stated that the reduced order observer improves the

dynamic response of the given system.

CONCLUSION

In this project, automatic generation control of the power system after

deregulation including bilateral contracts is investigated. In a practical environment

some of the state variable in AGC system such as output of governors, ACE or

integration of ACE, are not measurable. Because of this, a reduced order observer is

proposed for estimation of un-measurable states.

In order to demonstrate the effectiveness of the proposed method, the

control strategy described, is applied to the deregulated power system for AGC with

two areas.

This controller by using the states that are estimated allocates generating

unit’s output according to a deregulation scenario. The performance of the proposed

controller is evaluated through the simulation of two area power system.



Analysis reveals that the proposed technique gives good results and uses of

this method reduce the peak deviations of frequencies, tie-line power, time error and

inadvertent interchange. It can be concluded that the application of reduced order

observer controller to AGC of interconnected power system will be provided a

practical viewpoint. Also this method can be used in a large AGC power system as a

local estimator.

BIBLIOGRAPHY

Elyas Rakshani and Javad Sadeh, “Simulation of two-area AGC

system in a competitive environment using reduced order observer

method,” IEEE Trans. on Power systems, April, 2008.

O. I. Elgerd and C. E. Fosha, “Optimum megawatt-frequency control

of multi-area electric energy systems,” IEEE Trans. on Power

Apparatus and Systems, vol. PAS-89, pp. 556-563, Apr. 1970.

V. Donde, A. Pai and I. A. Hiskens, “Simulation and optimization in a

LFC system after deregulation,” IEEE Trans. on Power Systems,

vol. 16, no.3, pp. 481-489, Aug. 2001.



J. Kumar, Kah-Hoe Ng, G. Sheble, “AGC simulator for price-based

operation part 1: a model,” IEEE Trans. on Power Systems, vol. 12,

no. 2, May, 1997.

J. Kumar, Kah-Hoe Ng, G. Sheble, “AGC simulator for price-based

operation part 2: a model,” IEEE Trans. on Power Systems, vol. 12,

no. 2, May, 1997.

N. Jaleeli et al., “Understanding automatic generation control,” IEEE Trans. on Power Systems, vol. 7, no. 3, pp. 1106-1112, Aug, 1992.

P. Kunder, Power system stability and control, USA: McGraw-Hill;

1994.

H. Saadat, Power system analysis, USA: McGraw-Hill; 1999.

K. Sedigh, Modern Control Systems, University of Tehran Press,

2003.


simulation of two area agc system in a competitive environment-07

Documents

sri sai institute

vertically

vertically

area agc system

independent

deregulated

independent

state space