INTRODUCTION
Among ancillary services which should be procured in a power system, Spinning
Reserve (SR) has a significant importance to support system reliability. Spinning
Reserve (SR) is considered to satisfy the system loads in a sudden outage in
generating units and/or transmission lines as well as unforeseen increase in
load demand (Shahidehpour and Alomoush, 2001). In deregulated
power markets, satisfying a desired level of reliability; unit’s contribution
for energy production and SR procurement should be based upon minimizing total
costs of energy and SR dispatching. Generally two methods for energy and SR
dispatching are addressed the socalled Sequential Dispatch (SD) and Joint Dispatch
(JD). In SD regardless of considering the price of SR, at first energy is dispatched
optimally and then from the remained capacity of all units, SR can be dispatched
(Song and Wang, 2003). It might be said that SD method
may conclude two problems in satisfying real power demand and Spinning Reserve
Requirement (SRR). Since in SD method at first energy is dispatched, maximum
capacity of some units might be allocated only to energy and there is no more
capacity for allocating to SR. Under this condition although the other units
may have enough capacity for allocating to SR but because of their ramp up rate
constraint, they cannot satisfy system SRR which is infeasible. In some units,
where their energy prices are very closed while their SR prices are significantly
different, SD method will allocate most of energy to the cheaper units those
cannot have any chance to contribute for SR. Under this condition SR will be
procured by some expensive units where it may cause a noneconomic outcome.
In fact, the optimal allocation of energy and SR would be through a Joint Dispatch
(JD) technique, where in order to achieve a feasible as well as optimal solution
JD will consider the total procurement costs of energy and SR concurrently.
Transmission limit is one of the most important constraints which can
be considered in energy and SR dispatch problem in a real environment.
When energy and SR are dispatched without considering transmission limit
and only by minimizing the generation costs two problems may be happened.
It is according to achieve a particular pattern of energy production and
SR procurement. Firstly, based upon the prescribed allocated values for
energy and SR; in time of energy delivery some transmission lines might
be faced with an overload. Secondly, bottling of reserve can be occurred
in satisfying the allocated SR of all units that should guarantee system
reserve requirement. In bottling of reserve problem, sum of allocated
energy and SR to a typical unit may be bigger than the transmission lines
capacities that connect this unit to the system. Since there is a reserve
capacity that cannot be delivered, therefore the energy generation and
SR procurement pattern without considering transmission limit seems to
be infeasible.
A hybrid real genetic algorithm method is proposed by Baskar
et al. (2003) for solving the economic dispatch problem with multiple
fuel options. A method proposed by Chen et al. (2003)
addresses a joint dispatch for energy and SR considering a conventional optimal
power flow. A hybrid deterministic/probabilistic approach is proposed for SR
allocation by FotuhiFiroozabad and RashidiNejad (2004).
Energy and SR joint dispatch technique based upon a dynamic optimal power flow
is proposed by Costa and Costa (2007). A comprehensive
memetic algorithm is applied for solving joint energy and SR dispatch by Hazrati
et al. (2007). A method is also presented for solving the infeasibility
problem of SD technique by Asadi et al. (2008).
In this study, a new methodology is proposed for solving such a nonconvex
problem via JDbased technique using genetic algorithm as an evolutionary
optimizer. In this study transmission limit constraint is considered to
prevent bottling of reserve problem by implementing a DC power flow.
PROBLEM DEFINITION AND MATHEMATICAL FORMULATION
Joint energy and spinning reserve dispatch (JD) can be formulated as a constrained
optimization problem. The objective function of JD is considered as minimization
of joint energy production and SR procurement costs (RashidiNejad
et al., 2002). A competitive dayahead market is assumed where suppliers
may offer their active power associated with prices both for energy and SR through
a quadratic scheme for energy and a singlepart bid scheme for SR, respectively.
The objective function of such an optimization problem can be written as:
where,
are energy generation and reserve provision costs, respectively, T is
the scheduling time horizon and N is the No. of generating units.
Energy price is assumed to be quadratic while SR price is assumed to
be linear. Therefore energy and reserve costs are expressed by Eq.
2 and 3, respectively.
where, a_{i}, b_{i} and c_{i} are generation cost coefficients
and P^{t}_{i} is energy amount of generator i at hour t. R^{t}_{i}
and d_{i} are reserve amount and its price for generator i at hour t,
respectively (Kothari and Dhillon, 2004). The optimization
problem is subjected to some constraints in which Eq. 4 is
the balance between supply and demand.
where,
is forecasted demand for hour t. Some physical constraints also can be
written as follows:
where,
are maximum and minimum generation capacity of generator i, respectively.
Spinning reserve limits are defined by Eq. 7 and 8.
where,
are ramp up rate of generator i and SR requirement at hour t, respectively.
Δt is response time for SR while
is maximum reserve capacity that is defined by Eq. 9.
Transmission limit constraint is considered as fallows:
where, P_{ij} is active power flow from bus i to bus j and
is maximum power flow limit of ijth transmission line. In fact, by considering
transmission constraint, the generation strategy is determined which pattern
of energy generation and SR procurement has minimum costs while overload
would not be happened in any transmission line.
SOLUTION METHODOLOGY
Genetic algorithm is a random and robust search technique that guides a population
of encoded solutions towards an optimum using the principles of natural evolution.

Fig. 1: 
The flowchart of proposed solution approach for DJESD 
This process is facilitated through a fitness evaluation procedure, which determines
the fitness value of each member of the population the socalled chromosome.
The robustness of GA and its capability across a broad range of problems make
GA as general problem solving techniques in many applications (Swarup
and Yamashiro, 2002). So, in this study according to the complexity of dynamical
joint energy and SR dispatch (DJESD), GA is used to solve this complicated and
nonconvex optimization problem. The flowchart of the proposed GAbased solution
approach for DJESD is shown in Fig. 1 that includes the following
steps:
Step 1: Initialization and coding: In this step goal, constraint
and variable ranges will be defined while continuous variables should
be converted to discrete variables. Then the range of discrete variables
must be indexed. Finally, based on the problem requirement, genomes, chromosomes
and population must be created. In this study, every chromosome is a random
case of unit’s energy production and SR procurement. In fact, the
major difference between the proposed dispatching technique and other
GA based dispatching methods is chromosomes coding. In the proposed method,
chromosomes are coded randomly based upon the allocated energy and SR
such that all constraints should be satisfied.
Step 2: Decoding: In this step, binary values of each chromosome
are decoded while real equivalent of energy production and SR procurement
are calculated for all chromosomes.
Step 3: Feasibility checking: In this step, according to the allocated
energy and SR for each chromosome, DC power flow will be executed considering
two different conditions both for checking an overload. Firstly, it is
considered that each unit will produce just the amount of its allocated
energy. Secondly, it is considered that the allocated amount of energy
as well as SR will be produced. Then for each chromosome according to
the results of DC power flow, the number of violated transmission lines
(n) can be determined.
Step 4: Fitness evaluation: In this step, the fitness value of
each chromosome should be calculated. Some constrains associated with
the optimization problem that has proper form, might be incorporated into
the objective function as penalty function.
Step 5: Defining penalty factor: In this step, for those chromosomes
which have violations, penalty term will be added to their costs (obtained
from step 4). At first the overloaded lines will be specified and then
a penalty term is calculated by using Eq. 11.
where, P_{m} is power flow of overloaded line m and
is its maximum power flow limit.
Step 6: Elitism: To prevent of missing the best chromosomes of present
population after mating operators (selection, crossover and mutation), elitism
is used (Reily et al., 2005). Hence, 5% of the present
population with the best fitness will be selected as elites.
Step 7: Mating: The mating process consists of three operators: selection,
crossover and mutation (Haupt and Haupt, 2004).
Step 8: Chromosomes modification: Since after mating process there
are some chromosomes which do not satisfy problem constraints, in this
step those chromosomes should be modified such that all constraints are
satisfied.
Step 9: New population: At this step, the present population must
be renewed. Five percent of new population is consisted of elites while
95% is consisted from the produced offspring.
Step 10: Convergence check: The end step will be terminated if
the tour counter reaches the maximum predefined number of iterations and
if it is not satisfied then it goes to step 2.
CASE STUDIES AND RESULTS ANALYSIS
The proposed methodology is implemented to a typical IEEE 30bus test
system (Fig. 2) with six generators. Generation data
and system lines data are shown in Table 13.
Forecasted demand curve for 24 h is shown in Fig. 3.
SRR for each hour is considered as 10% of total demand in that hour. The
response time for SR is assumed 10 min incorporated with Ten Minute Spinning
Reserve (TMSR).
Applying SD method: Here, SD method is applied on the above mentioned
test system. In SD method which is used in this study, lambda iteration technique
is used for energy dispatch which is a suitable when cost functions are quadratic.
On the other hand, a merit order technique is used for SR dispatch (Shahidehpour
and Alomoush, 2001). The results of applying SD method on the IEEE 30bus
system are shown in Fig. 4.
As it is shown in Fig. 4, SD method cannot obtain a
feasible pattern for energy production and SR procurement from 15 to 21
h.The exact values of the allocated energy and SR using SD method are
shown in Table 4. In those hours, the maximum capacity
of units A, E and F is allocated to energy, while units B, C and D according
to their ramp up rate constraint cannot satisfy the SRR.
Applying JD method without transmission limit constraint: Here,
proposed JD method is applied to the IEEE 30bus system but transmission
limit constraint is neglected.
Table 1: 
Generation data for IEEE 30bus system 

Table 2: 
The percentage of system load at each bus 


Fig. 2: 
IEEE 30bus system 
Table 4: 
Allocated energy and SR to the units by using SD method
from 15 to 21 h 


Fig. 3: 
Forecasted demand curve for 24 h 
The solution methodology of JD without
transmission limit is the same as the algorithm with transmission limit
without considering step 3 and 5. The results of applying this method
are shown in Fig. 5. The exact values for the allocated
energy and SR to the units from 15 to 21 h are shown in Table
5. The obtained results show that when JD method is used, infeasibility
problem is not happened.
Energy production and SR procurement costs at each hour are shown in
Table 6 both for SD method and proposed JD method without
transmission limit. Because SD cannot find a feasible solution for energy
and SR dispatch from 15 to 21 h, therefore energy production and SR procurement
costs of those hours could not be calculated and shown by NF (not feasible).

Fig. 4: 
Scheduling of energy production and SR procurement by
using SD method, (a) generator A, (b) generator B, (c) generator C,
(d) generator D, (e) generator E and (f) generator F 
Table 5: 
Allocated energy and SR to the units by using JD method
from 15 to 21 h 

As shown in Table 6, energy production and SR procurement
costs of the proposed JD method is lower than SD method except for 17
h that costs of both methods are equal.

Fig. 5: 
Scheduling of energy production and SR procurement by
using JD method without transmission limit, (a) generator A, (b) generator
B, (c) generator C, (d) generator D, (e) generator E and (f) generator
F 
Table 6: 
Energy production and SR procurement cost 

Applying JD method with transmission limit constraint: Here, proposed
JD method with transmission limit is applied on the IEEE 30bus system.
The results of applying this method are shown in Fig. 6.
According to Table 3, maximum capacity of lines 911
and 1213 which connect units E and F to the system are 90 and 95 MW,
respectively. Therefore sum of the allocated energy and SR to these units
should not be more than transmission limits of connection lines, otherwise
bottling of reserve might be happened. By comparison between Fig.
5 and 6 it is shown that when transmission limit
constraint is neglected, in the most hours sum of allocated energy and
SR to units E and F is bigger than their connection transmission line
limit but this problem was not happened in any hours when transmission
limit is considered. In other word, these results show that the proposed
JD method with transmission limit can prevent bottling of reserve in all
hours.
In peak load hour, the allocated energy and SR to the units by using
the proposed JD without/with transmission limit are shown in Table
7 for 19 h.

Fig. 6: 
Scheduling of energy production and SR procurement by
using JD method with transmission limit, (a) generator A, (b) generator
B, (c) generator C, (d) generator D, (e) generator E and (f) generator
F 
Table 7: 
Allocated energy and SR using JD method with/without
transmission limit for peak load hour 

According to these values, DC power flow is executed in
two cases both with and without transmission limit. Firstly, it is considered
that each unit will produce just the amount of its allocated energy. Secondly,
it is considered that the allocated amount of energy as well as SR will
be produced. Results of applying DC power flow are shown in Table
8 and 9, where, is power flow from bus i to bus j only for energy production, is power flow from bus i to bus j for sum of energy and SR and is transmission limit of this line.
As shown in Table 8 and 9, when energy
and SR are dispatched without transmission limit, if generators tend to produce
just their allocated energy, overload is happened in lines of 911 and 1213.
Also when they want to produce their allocated SR, overload is happened in lines
of 1215, 1518 and 1523 as well. By comparing Table 8 and
9, it is observed that this problem is solved by using the
proposed JD method even having transmission line limits.
Total costs of energy production and SR procurement in 24 h is 113396.56
$ when transmission limits are neglected and it is 114825.11 $ when transmission
limits are considered. It is seen that when transmission limits are considered,
total costs is increased in about 1.26%. On the other hand, because of
transmission limit it is impossible for the cheap generators (E and F)
to use their maximum capacity for energy generation and SR procurement.
Therefore, we must allocate more energy to the expensive generators in
order to satisfy demand in all hours.
Table 8: 
DC power flow results for 19 h considering energy and
SR pattern via JD method without transmission limit 

Table 9: 
DC power flow results for 19 h considering energy and
SR pattern via JD method with transmission limit 

CONCLUSION
In this study, two general methods for energy and SR dispatch are presented.
It is shown that SD method is not a proper technique for energy and SR
dispatch because of two fundamental problems might be encountered. Therefore,
in this study a new joint algorithm associated with a GAbased technique
is proposed for energy and SR joint dispatch, while transmission line
limit is considered. The results of applying the proposed method for scheduling
a 6 unit show that the proposed method can offer a better solution in
comparison with the sequential dispatch method. It is also shown that
the proposed method can prevent happening the bottling of reserve problem
and overload in the lines properly. Significant simulation results presents
the effectiveness of the proposed methodology especially in a restructured
electricity environment.