Economic dispatch

Economic Dispatch

University of Turkish Aeronautical AssociationFaculty of Engineering

EEE department

TURKEY - ANKARA 2016

Eng. Hussein Ali Hussein

Presented by

Eng. Omar Sagban Taghi Eng. Ayad Tahseen Abdul hafedh

EEE 586

CONTENTS Introduction .

Economic dispatch neglecting losses and no generator limits.

Conclusion.

Problems of economic operation. Unit commitment. Operation cost of a thermal plant .

2/44Economic Dispatch

Different constraints in economic load dispatch .

Economic dispatch in power system interconnection .

Economic dispatch neglecting losses and including generator limits.

Introduction.


In a practical power system, the power plants are not located at the same distance from the center of loads and their fuel costs are different. Also, under normal operating conditions, the generation capacity is more than the total load demand and losses. Thus, there are many options for scheduling generation.

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Also, In an interconnected power system, the objective is to find the real and reactive power scheduling of each power plant in such a way as to minimize the operating cost.

This means that the generator's real and reactive power are allowed to vary within certain limits so as to meet a particular load demand with minimum fuel cost. This is called the optimal power flow (OPF) problem.

Introduction.


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Introduction.


The OPF (optimal power flow ) is used to optimize the power flow solution of large scale power system. This is done by minimizing selected objective functions while maintaining an acceptable system performance in terms of generator capability limits and the output of the compensating devices.

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Introduction.


The cost of operation varies from generator to generator based on factors such as the type of fuel used, efficiency of the generator and start-up costs.

As energy demand increases, generators that are more expensive to operate are used.

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Introduction.


In this presentation we will deal with the thermal power plants, because it is the most widely used, especially in our stations.

Economic dispatch depend on the types of the plants in each system .

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Problems of economic operation.


The economic operation can be subdivided into two

parts:

The problems of optimal power flow

Problems of the economic dispatch

which deals with determining the output power of each plant to meet the specified load in such away

that overall cost is minimized.

which deals with minimum loss delivery where the power flow is optimized.

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Unit commitment.

Economic Dispatch

The unit commitment problem (UC) in electrical power production is a large family of mathematical optimization problems where the production of a set of electrical generators is coordinated in order to achieve some common target, usually either match the energy demand at minimum cost or maximize revenues from energy production. This is necessary because it is difficult to store electrical energy on a scale comparable with normal consumption

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Constraints in unit commitment.

Economic Dispatch

1- Spinning reserve:

It is the total amount of generation available from all unit synchronized on the system minus the present load and loss being supplied.

It is must be carried so that the lost of one or more unit doesn't cause too far drop in system frequency.

It is must be allocated among fast responding units and slow responding units . This allow the automatic generation control system to restore the specified frequency .

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Constraints in unit commitment.

Economic Dispatch

Minimum up time: once the unit is running , it shouldn't turn off immediately.

2- Thermal unit constraints:

Minimum down time: once the unit is de-committed , it cannot be turn on immediately .

Crew constraint: if a plant consists of two or more units , they cannot be turn on at the same times since there are not enough crew members to attend both units while starting up .

3- Hydro-constraints: Unit commitments cannot be completely separated from scheduling of hydro-units .4- Must run constraint : some units are given a must-run status during certain times of the year .5-Fuel constraint: Some plants cannot be operated due to deficient fuel supply.

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Operation cost of a thermal plant :

Economic Dispatch

The factors influencing power generation at minimum cost are operating efficiencies of generators, fuel cost, and transmission losses.

The most efficient generator in the system does not guarantee minimum cost as it may be located in an area where fuel cost is high.

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Economic Dispatch

Power plants consisting of several generating units are constructed investing huge amount of money, fuel cost, staff salary, interest and depreciation charges and maintenance cost are some of the components of operating cost.

Also, if the plant is located far from the load center, transmission losses may be considerably higher and hence the plant may be overly uneconomical. Hence, the problem is to determine the generation of different plants such that the total operating cost is minimum.

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Economic Dispatch

Fuel cost is the major portion of operating cost and it can be controlled. Therefore, we shall consider the fuel cost alone for further consideration.

The input to the thermal plant is generally measured in Btu/h, and the output is measured in MW. A simplified input-output curve of a thermal unit known as heat-rate curve.

Input G

A/P

Steam turbineBoiler fuel

Output

Auxiliary power system

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Economic Dispatch

The input-output curve of a thermal unit known as heat-rate curve as shown in Fig.

Converting the ordinate of heat-rate curve from Btu/h to $/h results in the fuel cost curve shown in Figure .In all practical cases, the fuel cost of generator ith can be represented as a quadratic function of real power generation:

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Economic Dispatch

An important characteristic is obtained by plotting the derivative of the fuel-cost curve versus the real power. This is known as the incremental fuel-cost curve (λ) shown in Figure.

The incremental fuel cost curve is a measure of how costly it will be to produce the next increment of power.

The total operating cost includes the fuel cost and the cost of labor, supplies and maintenance. These costs are assumed to be a fixed percentage of the fuel cost and are generally included in the incremental fuel-cost curve.

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Economic Dispatch

An economic dispatch schedule for assigning loads to each unit in a plant can be prepared by :

A. Assuming various values of total plant output. B. Calculating the corresponding incremental fuel cost λ of the plant. C. Substituting the value of λ for (λ1, λ2…..) in the equation for the incremental fuel cost

of each unit to calculate its output.

For a plant with two units having no transmission losses operating under economic load distribution the λ of the plant equals λi of each unit, and so

λ= dC1/dP1 = 2γ1 P1+β1 ; λ= dC2/dP2 = 2γ2 P2+β2;P1 + P2 = PD where PD = total load demand

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Different constraints in economic load dispatch

Economic Dispatch

- Voltage constraints:

Vmin ≤ V ≤ Vmax ᴓmin ≤ ᴓ ≤ ᴓmax Where ᴓ is the angle of the voltage

- Generator constraints: KVA loading of generator should not exceed prescribed value :

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Different constraints in economic load dispatch

Economic Dispatch

- Running spare capacity constraints:

- Transmission line constraints: Flow of power through transmission line

should less than its thermal capacity.

This constraints are needed to meet forced outage of one or more alternators in the system and also unexpected load on the system .

- Transmission line losses constraints .

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Economic Dispatch

The simplest economic dispatch problem is the case when transmission line losses are neglected.

That is, the problem model does not consider system configuration and line impedances. In essence, the model assumes that the system is only one bus with all generation and loads connected to it as shown schematically in Figure .

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Economic Dispatch

Since transmission losses are neglected, the total demand PD is the sum of all generation. A cost function Ci is assumed to be known for each plant.

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Economic Dispatch

The problem is to find the real power generation for each plant such that the objective function (total production cost) as defined by the equation is minimum , subject to the constraint:

where Ct is the total production cost, Ci is the production cost of ith plant, P is the generation of ith plant, PD is the total load demand, and ng is the total number of dispatchable generating plants. A typical approach is to augment the constraints into objective function by using the Lagrange multipliers.

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Economic Dispatch

The minimum of this unconstrained function is found at the point where the partials of the function to its variables are zero.

Since :

Then : Therefore the condition for optimum dispatch is :

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Economic Dispatch

In summary, when losses are neglected with no generator limits, for most economic operation, all plants must operate at equal incremental production cost while satisfying the equality constraint given by:

The incremental cost ($/MW.h) :

In order to find the solution, from these two equations:

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Economic Dispatch

Example : system consists of three plants ,

+ + /$(h )+𝑻𝒐𝒕𝒂𝒍𝒅𝒆𝒎𝒂𝒏𝒅𝑷 𝑫=𝟏𝟖𝟎𝟎𝐌𝐖

P1 P2 P30

100

200

300

400

500

600

700

800

600 600 600614.8

493.2

691.9

Power of each plant (MW)

without diapatch with dispatch

COST1 COST21542015440154601548015500155201554015560155801560015620

15600

15490

Total cost ($/h)

without dispach with dispatach

- The fuel cost functions for three thermal plants in $/h are given by:

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Economic Dispatch

The power output of any generator should not exceed its rating nor should it be below that necessary for stable boiler operation.

Thus, the generations are restricted to lie within given minimum and maximum limits. The problem is to find the real power generation for each plant such that the objective function ( total production cost) as defined by these equations are minimum.

And the inequality constraints given by :

Where Pi(min) and Pi(max) are the minimum and maximum generating limits respectively for plant i.

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Economic Dispatch

The Lagrangian conditions complement to include the inequality constraints as additional terms. The necessary conditions for the optimal dispatch with losses neglected becomes:

The numerical solution is the same as before. That is, for an estimated (λ).

As soon as any plant reaches a maximum or minimum, the plant becomes pegged at the limit. In effect, the plant output becomes a constant, and only the unviolated plants must operate at equal incremental cost.

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Economic Dispatch

Example : system consists of three plants ,

+

++

- The fuel cost functions for three thermal plants in $/h are given by:

P1 P2 P30

50100150200250300350400450500 450

325

200

470

305

200


without limits(λ=8.7) with limits(λ=9.1)

𝑻𝒐𝒕𝒂𝒍𝒅𝒆𝒎𝒂𝒏𝒅𝑷 𝑫=𝟗𝟕𝟓𝐌𝐖

COST1 COST28210

8215

8220

8225

8230

8235

8240

8220

8236

Total cost ($/h)

without limits with limits

470 ≤P1 ≤ 600

300 ≤P2 ≤ 500

150 ≤P3 ≤ 200

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Economic dispatch including transmission losses.

Economic Dispatch

When transmission distances are very small and load density is very high, transmission losses may be neglected and the optimal dispatch of generation is achieved with all plants operating at equal incremental production cost.

However, in a large interconnected network where power is transmitted over long distances with low load density areas, transmission losses are a major factor and affect the optimum dispatch of generation.

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Economic Dispatch

The associated mathematical definition becomes:

And the Lagrangian function can be written as:

The minimum point occurs when : or

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Economic Dispatch

Rearrange this equation :

The incremental fuel-cost (λ) becomes :

where Li is known as the penalty factor of plant i and is given by :

or

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Economic Dispatch

Example : system consists of three thermal plants , - The fuel cost functions for three thermal plants in $/h are given by:+

++

𝑻𝒐𝒕𝒂𝒍𝒅𝒆𝒎𝒂𝒏𝒅 𝑷𝑫=𝟖𝟓𝟎𝐌𝐖

++

P1 P2 P3 P(losses) Total power generated

0100200300400500600700800900

1000

393.2 334.6

122.20

850

434.13299.9

130.7

14.73

864.73

Power (MW)

without TL.losses(λ=9.14) withTL.losses(λ=9.53)

Total cost8100

8150

8200

8250

8300

8350

8194

8334

Total cost ($/h)

without TL.losses(λ=9.14) withTL.losses(λ=9.53)

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Economic dispatch in a power system interconnection .

Economic Dispatch

- Why do we need to the power system interconnection ? Interconnection makes the system

more reliable : since the loss of a generation plant can be covered from spinning reserve among of other units. Hence if the unit is lost in one control area governing action from units in all connected areas will increase generation output to make up the deficit unit until it is brought online again.

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Economic Dispatch

Better economy of operation is attained when utilities are interconnected. This situation take place if the interconnected system works at different incremental cost.

The interconnected system will generally require a smaller generator capacity.

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- Why do we need to the power system interconnection ?

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Economic Dispatch

1- Capacity interconnection : Normally, a power system will add generation to make sure that the available capacity of unit it has equal its predicted peak load plus a reserve to cover unit outages , if for some reason this criterion cannot be met, the system may enter into a capacity agreement with a neighboring system , provided that neighboring system has surplus capacity beyond what it needs to supply its own peak load and maintains its own reserve.

Types of the power interconnection .

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Economic Dispatch

Types of the power interconnection .

2- Diversity interconnection : Daily diversity interchange arrangement may be made between two large system covering operating areas to span different time zones.

This type of interconnection can take place between systems whose peak loads depend on seasons of the year .

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Economic Dispatch

Types of the power interconnection .3- Energy banking : Energy banking agreement usually occurs when a predominantly hydro system is interchange to a predominately thermal system.

During high water run off periods , the hydro system may have energy to spare and sell it to the thermal system . Conversely the hydro system may also need to import energy during periods of low run off .

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Economic Dispatch

Types of the power interconnection .4- Emergency power interconnection : It is very likely that at some future time a power system will have in series of generation failure that requires it to import power.

5- Inadvertent power exchange: The AGC (automatic generation control) systems of utilities are not perfect device with the result so that the error in controlling interchange result occurs in a significant amount of energy.

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Economic Dispatch

Since the power system interconnection is a large system and also has many constraints like (transmission line capability constraint, transmission line losses constraints ,limit generation and frequency constraint) ,so that we have to choose the optimal option of the economic dispatch .

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Economic Dispatch

Example : Three areas are interconnected with each other,

+

+

+

- The fuel cost functions for the three areas in $/h are given by:

100 ≤Pi ≤ 400

Area 1

Area 2

Area 3PD=200MW

PD=200MW

PD=200MW

TL(limit)=75MW TL(limit) =75MW

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Economic Dispatch

Example : Three areas are interconnected with each other,

P1 P2 P30

50

100

150

200

250

300

350

200 200 200200

300

100

191.67

283.33

125


without inter with inte. and without TL.limitscost

2800

2900

3000

3100

3200

3300

3400

3500

3400

3000

3258

Total cost ($/h)

without inter.and TL.limits withinter. And without TL.limits

With inter.and TL.limits With inter.and TL.limits

TL(limit)=75MW

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PD (each area)=200MW100 ≤Pi ≤ 400

Conclusion.

4- The case of economic dispatch without transmission losses and generator constraints gives the better result.

3- Penalty factors are used to consider the impact of losses in a large interconnected network where power is transmitted over long distances .

2- The unit commitment is concerned with determining which units to turn on/off.

1- The economic dispatch is the operation of generation facilities to produce energy at the lowest cost.

Economic Dispatch

5- Interconnection power systems makes the system more reliable and better economic of operation .

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References .

Hadi Saadat, “Power system Analysis,” Tata McGraw Hill Publishing Company, New Delhi, 2002.

Asbfaq Husain, “Electrical power system,” CBS publishers and Distributers, Fifth Edition, 2007.

Nagendra Singh1, Yogendra Kumar2,” Constrained Economic Load Dispatch Using Evolutionary Technique” Asian Journal of Technology & Management Research [ISSN: 2249 –0892] Vol. 03 – Issue: 02 (Jul - Dec 2013).

Hardiansyah, “A Modified Particle Swarm Optimization Technique for Economic Load Dispatch with Valve-Point Effect” , I.J. IntelligentSystems and Applications, 2013, 07, 32-41 Published Online June 2013 in MECS DOI:10.5815/ijisa.2013.07.05.

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Thank you Contact information:

Eng. Hussein Ali Hussein

[email protected]

Eng. Ayad Tahseen Abdul hafedh

[email protected]

Eng. Omar Sagban Taghi

[email protected]

Economic Dispatch 44/44

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