Power Economic Dispatch --- A Brief Survey

7/29/2019 Power Economic Dispatch --- A Brief Survey

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CHAPTER 2

Power Economic Dispatch --- A Brief Survey

2.1 IntroductionPower Economic Dispatch is vital and essential daily optimization procedure in

the system operation. It is a constrained nonlinear optimization problem. This chapter

presents brief overview and literature survey on economic dispatch problem with focus on

GA based approaches. Final section gives review on economic dispatch using GA

independently and in hybrid form with some observations and potential avenues for

further investigations.

2.2 Power System Operational PlanningThe operational planning of the power system involves the best utilization of the

available energy resources subjected to various constraints to transfer electrical energy

from generating stations to the consumers with maximum safety of personal/equipment

without interruption of supply at minimum cost. In modern complex and highlyinterconnected power systems, the operational planning involves steps such as load

forecasting, unit commitment, economic dispatch, maintenance of system frequency and

declared voltage levels as well as interchanges among the interconnected systems in

power pools etc.

Figure 2.1 illustrates the operation and data flow in a modern power system on the

assumption of a fully automated power system based on real-time digital control [1].

There are three stages in system control, namely generator scheduling or unit

commitment, security analysis and economic dispatch.

Generator scheduling involves the hour-by-hour ordering of generator units on/offin the system to match the anticipated load and to allow a safety margin.


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With a given power system topology and number of generators on the bars,security analysis assesses the system response to a set of contingencies and

provides a set of constraints that should not be violated if the system is to remain

in secure state.

Economic dispatch orders the minute-to-minute loading of the connectedgenerating plant so that the cost of generation is a minimum with due respect to

the satisfaction of the security and other engineering constraints.

Load

forecasting

Unit commitment Security ana lysis Economic dispatch

System topology change

commandsData base

Generator s tartup

& shutdown

commands

State

estimation

Generator P & Q

loading commands

Measurements, switch

positions

Power system

Figure 2-1 Power System Control Activities

2.3 Economic Dispatch --- Literature SurveyEconomic dispatch is generation allocation problem and defined as the process of

calculating the generation of the generating units so that the system load is supplied

entirely and most economically subject to the satisfaction of the constraints [2].


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Historically economic dispatch is being carried out since 1920. It was the time

when engineers were concerned with the problem of economic allocation of generation or

the proper division of the load among the generating units available. The developments in

ED may be listed [2] as:

1. Prior to 1930, the methods in use includes: the base load method and bestpoint loading

2. It was recognized as early as 1930, that the incremental method, later knownas the equal incremental method, yielded the most economic results.

3. The analogue computer was developed to solve the coordination equations.4. A transmission loss penalty factor computer was developed in 1954.5. An electronic differential analyzer was developed and used in ED for both off-

line and on-line use by 1955.

6. The digital computer was investigated in 1954 for ED and is being used todate.

H. H. Happ presented [2] comprehensive survey on economic dispatch. The

survey covers the following aspects:

Developments in Economic dispatch since early 1920s. Step by step developments taking into account the effect of transmission loss in

economic dispatch problem.

Multi-area concepts in economic dispatch. Valve point loading Optimal load flow

Three part series [3-5] presented by IEEE working group 71-2 (W.G. on

Operating Economics) describes the major security economy functions and bibliography

from 1959 to 1977. Part I [3] contains the descriptions of major economy-security

functions; Part II [4] & Part III [5] give the bibliography. The economic dispatch has been

addressed under Real Time Operation function with categories as: 1) Economic

Dispatch [RE], 2) Security Dispatch [RS], and 3) Environmental Dispatch [RV].

B .H. Chowdhury, et al. [6] presented a survey of papers and reports addressing

various aspects of economic dispatch during the period 1977-88. The survey has been

focused under the following four areas of economic dispatch:


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Optimal power flow. Economic dispatch in relation to AGC. Dynamic dispatch. Economic dispatch with non-conventional generation sources.

Mathematical programming based approaches for ED may be classified as:

1. Merit Order approach (Old Method)2. Equal Incremental Cost Criterion (widely used)3. Linear Programming (Easy Constraint Handling)4. Dynamic Programming (Curse of dimensionality)5. Nonlinear Programming

2.3.1 Thermal Machines Cost Curve in Economic DispatchGenerators in system operation studies are represented by input/output cost

curves. It is the standard industrial practice that the fuel cost of generator is represented

by polynomial [7] for Economic Dispatch Computation (EDC). The key issue is to

determine the degree and the coefficients such that the error between the polynomial and

test data is sufficiently low. Traditionally, in the EDC, the cost function for each

generator has been approximately represented by a single quadratic function. This curve

is convex in nature. Various mathematical and optimization techniques have been applied

to solve ED problem. Most of these are calculus-based optimization algorithms that are

based on successive linearization and use the first and second order differentiations of

objective function and its constraints equations as the search direction. They usually

require heat input, power output characteristics of generators to be of monotonically

increasing nature or of piecewise linearity.

2.3.2 Nonconvex Cost CurvePresent day large power generating units with multi-valves steam turbines exhibit

a large variation in the input-output characteristic functions, thus nonconvexity appears in

the characteristic curves. Two major nonconvex economic dispatch problems may be

listed as [8]:

1. Economic dispatch with piecewise quadratic cost function (EDPQ)2. Economic dispatch with prohibited operating zones (EDPO).


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2.3.2.1Piecewise Quadratic Cost Curvea. Valve Point Effect

The valve point effects [9], owing to wire drawing as each steam admission valvestarts to open, typically produce a ripple like heat rate curve, which is non-smooth

in nature as shown in Figure 2.2. This type of the characteristic must be used to

schedule steam units accurately, but it can not be used in traditional optimization

methods because it does not meet the convex condition. Smooth quadratic

function approximation of cost curves is used in classical economic dispatch.

Figure 2-2 Value Point Effect

b. Multiple Fuel MixSome generation units especially those units which are supplied with multiple fuel

sources (gas and oil) are faced with the problem of determining the most

economical fuel to burn. As fossil fuel costs increase, it becomes even more

important to have a good model for the production cost of each generator.

Therefore a more accurate formulation [10] is obtained for the ED problem by

using hybrid cost function and hybrid incremental cost function and expressing

these generation cost function as a piecewise quadratic function and linear

function respectively as shown in Figure 2.3.

Figure 2-3 Hybrid Cost & Incremental Cost


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2.3.2.2Prohibited Operating ZoneDue to the physical restrictions of power plant components (faults in the machines

themselves or the associated auxiliaries), the whole of the unit operating range is not

always available for load allocation; and generating units may have prohibited operating

zones lying between their minimum and maximum power outputs [11]. The operation in

these zones may result in amplification of vibrations in a shaft bearing which should be

avoided in practical application. Usually, each prohibited region makes the decision space

separate into disjoint subsets which then constitute a non-convex decision space.

Therefore, the corresponding economic dispatch problem becomes a non-convex

optimization problem [8].

2.3.3 Economic Dispatch Based on Traditional Optimization--- BottlenecksGenerally the economic dispatch problem is solved as convex optimization

problem. Mathematical programming based optimization techniques have been developed

to solve economic dispatch (ED) problem. They usually require heat input, power output

characteristics of generators to be of monotonically increasing nature or of piecewise

linearity. These simplifying assumptions result in an inaccurate dispatch.

The actual economic dispatch problem is non-convex in nature due valve point

effect, multiple fuels and prohibited operating zones. Dynamic programming [12] has

been used to solve this problem, but due to curse of dimensionality it has limitations.

Thus for the accurate dispatch, the approaches independent of restrictions such as

continuity, differentiability, convexity are potential solution methodologies.

2.3.4 Genetic Algorithm Based Economic DispatchThe power engineering community has been studying the feasibility and

application of Artificial intelligence tools for efficient solution of complex power system

problems. AI tools such as 1) Artificial Neural Network (ANN), 2) Expert Systems, 3)

Evolutionary Computation, and 4) Fuzzy Logic have been developed to formulate and

solve the convex and non-convex economic dispatch problem.

Genetic algorithm (GA) is one of the most popular paradigms of evolutionary

computation. It has been used to solve the economic dispatch problem independently and


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in conjunction with other AI tools and optimization approaches. It has the superior global

searching capability in a complex searching surface using little information of searching

space, such as derivative, continuity thus providing potential tool for real economic

dispatch problem.

Genetic algorithm has inherent ability to reach the global minimum region of

search space in a short or affordable time [13-14]. But at the same time the disadvantages

are: 1) long computational time [15-16], 2) convergence speed near the global optimum

becomes slow, 3) provide near optimal solution [16] or non-convergence to global

solution [17]. There are several ways by which the performance of GA can be enhanced

[18]. Hybrid approach is one of the methodologies used efficiently for producing quality

results. The objective of hybridization is to overcome the weakness of one approach

during its application with the strengths of other by appropriately integrating them.

In the discussion to follow in this section brief review on GA based approaches

has been presented.

In 1993, Yoshimi, et al. [19] mapped ED problem in binary coded Genetic

Algorithm (GA) environment using typical reproduction operator crossover and mutation.

15-machine test system has been used for performance evaluation of GA in terms of

objective function and equality constraints satisfaction for four different case studies and

established the fact that GA performs function optimization in an adaptive manner so as

to schedule the power generation in order to minimize objective function.

In 1993, Walters, et al. [9] has used Simple genetic algorithm (SGA) with two

different encoding schemes for solving the ED problem including valve point effect. The

SGA has been tested for ED problem with & without losses for smooth and non-smooth

cost curves using three machine test system for five different cases by comparing the

results obtained from dynamic programming technique. He made useful observations

regarding the GA parameters during analysis and concluded that GA has the ability to

handle any type of unit characteristics.

In 1994, H. Ma, et al. [20] presented genetic algorithm based solution for ill

structured and multimodal economic dispatch problem including transmission loss


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considering compensating generation plan provided in the Clean Air Act 1990. The

proposed algorithm has been tested on 9-units system (including 2 hydro units with fixed

outputs).

In 1994, Bakirtzis, et al. [21] presented two genetic algorithms GAI & GAII for

the solutions of the economic dispatch problem. Test results with systems of up to 72

generating units with nonconvex cost functions show that both genetic algorithms

outperform the dynamic programming solution to the economic dispatch problem.

However, the solution time of GA-II is system dependent and increases linearly with the

size of system.

In 1995, Po-Hung, et al. [22] presented genetic algorithm based approach for

large-scale economic dispatch subject to the network losses, ramp rate limits and

prohibited zone avoidance. He has selected the encoding scheme such that chromosome

contains only an encoding of the normalized system incremental cost thus making

chromosome size independent of number of units. This feature has been exploited as an

edge for large-scale economic dispatch. The two test systems: 3 machines system and 40

units Tai power systems have been used for demonstration of the approach. The

comparison of results with lambda iteration method proved that proposed approach is

fast, robust in large systems.

In 1995, Sheble, et al. [23] presented genetic algorithm based solution for

economic dispatch with a view to get around the problems in classical optimization

theory. He proposed the techniques such as mutation prediction, elitism, interval

approximation and penalty factors to enhance the program efficiency and accuracy. Three

units test system has been test for Economic dispatch solution using proposed algorithm.

In 1996, P. Y. Wang, et al. [24] presented fuzzy logic controlled genetic algorithm

for economic dispatch problem. Two fuzzy logic controllers for adoptively adjustment

GA parameters (crossover rate and mutation rate) have been proposed. Six generators

system has been solved for economic dispatch using the proposed algorithm and

compared the results with conventional GA.

In 1996, Orero, et al. [25] has developed the genetic algorithm solution for

nonconvex economic dispatch problem taking into account the prohibited operating zones


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of the generators. Two different implementations of genetic algorithms: Standard Genetic

Algorithm & Deterministic Crowding Genetic Algorithm has been presented with a view

to improve the performance (--- robustness and few parameter settings) of genetic

algorithm. 15 generators practical power system with 4 of the units up to three prohibited

operating zones system has been tested on the proposed approaches.

In 1997, Li, et al. [26] investigated the capability of genetic algorithms on the

ramping rate constrained DED problem on 25 generators practical power supply system --

- Northern Ireland Supply (NIE). It has been established that the ramping rate constraint

not only put no additional burden on the genetic search, but also forced the search to

move within the operating feasible region, and gives smoother and more economical

operational strategy for the whole dispatch period. However, a too strict ramping rate

constraint will prevent a GA from obtaining an economic, feasible solution within a

reasonable time. An investigation into choice of appropriate ramping rates for the

generator units in a power system can be time consuming, but highly rewarding.

In 1997, Song, et al. [27] presented the application of a fuzzy logic controlled

genetic algorithm (FCGA) to environmental/economic dispatch. Two fuzzy controllers

have been designed to adaptively adjust the crossover probability and mutation rate

during the optimization process based on some heuristics. For the demonstration of

algorithm six machines system has been solved for economic load dispatch problem. The

results have been compared with conventional GA and Newton-Raphson Method for the

performance evaluation of proposed approach. It has also been recommended that this

algorithm can be applied to wide range of optimization problems.

In 1997, Song, et al. [28] proposed an advanced engineered-conditioning genetic

algorithm (AEC-GA) with a view to improve the performance of GA. This approach uses

combination strategy using local search algorithms and genetic algorithms. In addition to

this elite policy, adaptive mutation prediction, nonlinear fitness mapping and different

crossover techniques have also been explored. The proposed algorithm has been

demonstrated by solving the power economic dispatch problem. The six units test system

results have been for its validation.


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In 1998, Chira, et al. [29] has developed genetic algorithm based economic

dispatch solution for eastern region of Electricity Generating Authority of Thailand

(EGAT) system by using piecewise model of cost characteristics for the combined cycle

and the cogeneration power plants in the system. Conventional & parallel micro genetic

algorithms have been used for the solution with result that parallel micro genetic

algorithm offers faster convergence.

In 2000, Angela, et al. [30] developed framework GAFrame for constructing

genetic algorithms based on object oriented programming methodology. GAFrame

includes features: GUI, ease of use, code reusability, continuous & integer optimization

problem solution, flexible, and extensible. The two optimization problems: economic

dispatch and distribution system expansion planning has been solved by this framework

for validation of its features.

In 2001, T. Yalcinoz, et al. [31] proposed real coded genetic algorithm for the

solution of economic dispatch problem. Elitism, arithmetic crossover and mutation have

been used to generate solutions in successive generations. The approach has been tested

on 6 machine and 20 machine systems and results have been compared with an improved

Hopfield NN approach (IHN), a fuzzy logic controlled genetic algorithm (FLCGA), an

advance engineered-conditioning genetic approach (AECGA) and an advance Hopfield

NN approach (AHNN) and established the fact that the proposed technique improves the

quality of the solution.

In 2002, T. Yalcinoz, et al. [32] presented the environmental economic dispatch

problem using modified GA, which based on arithmetic crossover operator. The objective

function consists of three terms, which are the production cost and emissions functions.

The proposed algorithm has been tested on 3-unit system and a 10-unit system and results

compared with the taboo search (TS), the Hopfield NN and an improved Hopfield NN

approach.

In 2002, Ying-Yi, et al. [33] solved using binary coded GA for optimal dispatch

among multi-plant (cogeneration systems) with multicogenerators, which transmit MW to

designated buyers (load buses) via wheeling subject to the operation constraints in the

cogeneration systems and security constraints in the third party (transmission system


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owner). Varying weighting coefficients for penalty functions (constraint handling) and

determination of gene variables for GA has been adopted. The algorithm has been tested

on IEEE 30 and 118-bus systems. From the test results, it has been shown that the

computational time required strongly depends on the number of the gene variables

(Lagrange multipliers) instead of the system size. Also, the proposed method can

efficiently obtain the global optimum with the concept of equal Lagrange multiplier.

In 2002, Jarurote, et al. [34] proposed an algorithm based on parallel micro

genetic algorithm for the solution of ramp rate constrained economic dispatch neglecting

the transmission loss for generating units with non-monotonic & monotonic incremental

cost functions. The proposed algorithm was programmed on thirty-two-processor Bewulf

cluster subject to schedule processors, computational loads, and synchronization overhead

for the best performance. The speedup upper bounds and the synchronization overheads

on the Beowulf cluster for different system sizes and different migration frequencies have

been shown. Claim has been made that PMGA is viable to the online implementation of

the constrained ED due to substantial generator fuel cost savings and high speedup upper

bounds.

In 2002, Patricia, et al. [35] presented GA based solution for the operational

planning of hydro-thermal power systems to get around the deficiencies in nonlinear

programming based approaches. The paper presents an adaptation of the technique and an

actual application on the optimization of the operation planning for a cascaded system

composed by interconnected hydroelectric plants. The fact has been established that by

using GA approach, for each additional problem constraint, only the equation used to

define each individual performance needs to be modified and proposed approaches can be

an efficient alternative or complementary technique for the planning of Hydrothermal

power system operation.

In 2003, Ioannis, et al. developed [36] real coded GA for the solution of network

constrained Power economic Dispatch for minimizing the dispatch cost subject to branch

power flow limits. 52 buses Greek island of Crete system has been tested with convex

cost functions and nonconvex cost functions for proposed algorithm to establish that the

algorithm retained the advantages of the GAs over the traditional ED methods but also


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eliminated the main disadvantage of the binary coded GAs (long execution time) and thus

providing an efficient generic ED solution method.

In 2004, Liladhur, et al. [37] presented economic dispatch solution considering

valve point loading effect using simple genetic algorithm (SGA), SGA with generation-

apart elitism, SGA with atavism and atavistic genetic algorithm (AGA). These three

concepts have been compared on three test systems: 3-generator system, 13-generator

system and the standard IEEE 30-bus test system. It has been established that when

valve-point loading and ramping characteristics of the generators are taken into account,

AGA outperforms SGA, SGA with generation-apart elitism, SGA with atavism, Tabu

search and conventional Lagrangian multiplier method.

In 2004, Hosseini, et al. [38] discusses the centralized economic dispatch in

deregulated environment. Power economic dispatch problem has been using genetic

algorithm subject to the constraints such as are minimum and maximum power generation

of units, capacity of transmission lines and ramp rate limits. IEEE 30 bus system has been

tested for the proposed algorithm for its validation.

In 2005, Bakare, et al. [39] has made comparative investigation of both

conventional GA and micro-GA for Power economic dispatch problem using 6-bus IEEE

test system and 31-bus Nigerian grid Systems. The results obtained are satisfactory for

both approaches, but it is shown that the GA performed better than CGA with reference

to the economic and computational time (average of 62% time reduction) for Nigerian

system.

In 2005, Chao-Lung Chiang, et al. [40] presented genetic algorithm solution for

economic dispatch taking into account the valve point effect and multiple fuels

simultaneously with multiplier update (IGA_MU). Basically this algorithm is the

integration of the improved genetic algorithm (IGA) and the multiplier updating (MU).

The proposed algorithm has been demonstrated by applying separately on: 13 units test

system considering valve-point effects only, 10 units considering multiple fuels only, and

ten units addressing both valve-point effects and multiple fuels. By comparison of results

of proposed algorithm with conventional genetic algorithm with multiplier update, it has

been established the fact that IGA_MU is more effective and can apply to the real world

problems.


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Wong, et al. in [41] presented Simulated Annealing (SA) based economic dispatch

algorithm. The algorithm was demonstrated on three generating units system only. In

comparison with Zoom Dynamic Programming (ZDP) method [42] economic dispatch

results obtained for the test system are more economical. Subsequently in [43] four

algorithms ( two GA based algorithms, Basic Genetic Algorithms (BGA) and Incremental

Genetic Algorithm (IGA), two Genetic simulated annealing based algorithms GGA and

GAA2) have been presented to determine the optimal or near optimum solution of the ED

problem. By modifying step 3 of four steps BGA algorithm, an IGA algorithm has been

derived which can find global optimum solution earlier in the solution process than BGA.

To avoid premature convergence in IGA, hybrid algorithm GAA is developed by

combining IGA and simulated annealing. Further GAA2 is developed to deal with the

memory requirement by reducing the population size to 2. 13 Machine real life system

has been tested and established the fact GAA2 is superior than other algorithms.

Ongsakul, et al. [44] proposed the micro genetic algorithm based on migration and

merit order loading solutions (MGAM-MOL) for solving the constrained ED with linear

decreasing and decreasing staircase IC functions. MGAM-MOL used a merit order

loading (MOL) solution as a base solution to reduce the search effort to the optimal

solution. The MGAM-MOL solutions were less expensive than those obtained from

simple genetic algorithm (SGA), micro genetic algorithm (MGA), and MOL.

Ongsakul, et al. in [45] presented a genetic algorithm based on simulated

annealing solutions (GA-SA) to solve ramp rate constrained Dynamic Economic Dispatch

(DED) problems for generating units with non-monotonically and monotonically

increasing IC functions. As the transmission line losses are incorporated, GA-SA is tested

on the 10 generating unit systems and compared to the zoom brute force (ZBF), ZDP, SA,

local search (LS), genetic algorithm based on MOL solutions (GA-MOL), and MOL

methods. To illustrate the quality of GA-SA solutions on larger generating unit systems,

the algorithm has also been tested and compared to the others on the 20 and 40 generating

unit systems.

Yalcinoze, presented [46] hybrid genetic algorithm (HGA) for solving the

economic dispatch problem. The algorithm incorporates the solution produced by an

improved Hopfield neural network (NN) as a part of its initial population. Elitism,


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arithmetic crossover, and mutation are used in the GAs to generate successive sets of

possible operating policies. The technique improves the quality of the solution and

reduces the computation time, and is compared with the classical optimization technique,

an improved Hopfield NN approach (IHN), a fuzzy logic con-trolled GA (FLCGA), and

an improved GA (IGA).

Attaviriyanupap, et al. in [16] proposed hybrid methodology for solving DED.

The proposed method has been developed in such a way that a simple evolutionary

programming (EP) has been applied as a based level search, which can give a good

direction to the optimal global region, and a local search sequential quadratic

programming (SQP) has been used as a fine tuning to determine the optimal solution at

the final. A ten-unit test system with non-smooth fuel cost function has been used to

illustrate the effectiveness of the proposed method compared with those obtained from EP

and SQP alone.

Kumarappan, presented [47] Neuro hybrid Genetic Algorithm (GA) to solve an

economic dispatch problem. The algorithm has been proposed for minimum cost of

operating units. Working philosophy of algorithm is as: 1) Real Coded GA has been used

for global search 2) fine tunings by Tabu Search (TS) to direct the search towards the

optimal region and local optimization 3) For loss calculation Fast Decoupled Load Flow

(FDLF) conducted to find the losses by substituting the generation values to the

respective PV buses. Then the loss has been participated among all generating units using

participation factor method. Artificial Neural Networks (ANN) has been applied to the

Hybrid GA. The algorithm is tested on IEEE 6-bus system and 66-bus utility system.

2.3.4.1DiscussionThe focus of GA based approaches for economic dispatch solution is around the

aspects such as: convex [31] & nonconvex ED problem [9, 21, 22, 23, 25, 37],

environmental concern [20, 27, 32], power market [33,38] and handling of combined

cycle plant. Evolution model adopted includes: binary coded GA [9, 19, 20, 21, 22, 23]

with different schemes for picking bits in decoding step, real coded GA [31, 36], micro

GA [29] and parallel GA [34]. Standard test systems of various sizes in terms number of


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machines [9, 19, 20, 21, 22, 23, 25] and utility systems [29, 36, 39] have been used during

investigations.

In the deregulated environment where cost minimizations not only the objective,

but at the same time profit maximization is the also the concern. Fast and accurate

economic dispatch solution is as usual the requirement in deregulated scenario as well.

Despite the advances in GA based approaches, potential avenues for further exploration

may be listed as:

1. Flexible and extensible computational framework as common environment forimplementing economic dispatch algorithms.

2. Some methodology for GA parameters for economic dispatch.3. Mapping of biological mechanism in terms of GA operators in economic

dispatch problem.

4. Performance evaluation of GA evolution models for economic dispatchproblem.

5. Exploration of GA based ED approaches for the utility systems.6. Hybrid methodology is the useful tool for efficient solution by exploiting the

strengths of GA with the powers of other techniques by appropriate integration

of both the approaches. So this sector is the potential area for developing

simple fast and efficient GA based hybrid methodologies.

Power Economic Dispatch --- A Brief Survey

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