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Dynamical Joint Energy and Spinning Reserve Dispatch Considering Transmission Network Constraint



M. Asadi Bazardeh and M. Rashidi-Nejad
 
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ABSTRACT

This study is dealing with ancillary services procurement and pricing in the new environment of electricity market. Spinning reserve is one of the most important ancillary services needed for satisfying reliability requirements as well as desired level of security in power systems. In deregulated power markets, generally two methods for energy and spinning reserve dispatching are addressed the so-called sequential dispatch and joint dispatch. It can be said that the sequential dispatch method may not be even feasible as well as optimal because of the coupling between spinning reserve and energy capacity. Therefore, in this study, a new method is proposed for dynamical joint energy and reserve dispatch that can solve the bottling of reserve problem by considering transmission limits. A genetic algorithm as an evolutionary optimization technique is used to solve such a complicated and non-convex problem. The proposed methodology is applied to a typical IEEE 30-bus system, while simulation studies show the effectiveness of joint energy and spinning reserve dispatch in comparison with the sequential dispatch.

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  How to cite this article:

M. Asadi Bazardeh and M. Rashidi-Nejad, 2009. Dynamical Joint Energy and Spinning Reserve Dispatch Considering Transmission Network Constraint. Journal of Applied Sciences, 9: 1248-1257.

DOI: 10.3923/jas.2009.1248.1257

URL: https://scialert.net/abstract/?doi=jas.2009.1248.1257
 

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 so-called 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 non-economic 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 Fotuhi-Firoozabad and Rashidi-Nejad (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 non-convex problem via JD-based 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 (Rashidi-Nejad et al., 2002). A competitive day-ahead 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 single-part bid scheme for SR, respectively. The objective function of such an optimization problem can be written as:

Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint
(1)

where, Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint 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.

Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint
(2)

Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint
(3)

where, ai, bi and ci are generation cost coefficients and Pti is energy amount of generator i at hour t. Rti and di 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.

Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint
(4)

where, Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint is forecasted demand for hour t. Some physical constraints also can be written as follows:

Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint
(5)

Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint
(6)

where, Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint are maximum and minimum generation capacity of generator i, respectively. Spinning reserve limits are defined by Eq. 7 and 8.

Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint
(7)

Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint
(8)

where, Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint are ramp up rate of generator i and SR requirement at hour t, respectively. Δt is response time for SR while Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint is maximum reserve capacity that is defined by Eq. 9.

Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint
(9)

Transmission limit constraint is considered as fallows:

Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint
(10)

where, Pij is active power flow from bus i to bus j and Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint 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.

Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint
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 so-called 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 non-convex optimization problem. The flowchart of the proposed GA-based 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.

Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint
(11)

where, Pm is power flow of overloaded line m and Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint 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 30-bus test system (Fig. 2) with six generators. Generation data and system lines data are shown in Table 1-3. 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 30-bus 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 30-bus system but transmission limit constraint is neglected.

Table 1: Generation data for IEEE 30-bus system
Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint

Table 2: The percentage of system load at each bus
Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint

Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint
Fig. 2: IEEE 30-bus system

Table 3: Line data
Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint

Table 4: Allocated energy and SR to the units by using SD method from 15 to 21 h
Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint

Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint
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).

Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint
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
Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint

As shown in Table 6, energy production and SR procurement costs of the proposed JD method is lower than SD method except for 1-7 h that costs of both methods are equal.

Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint
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
Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint

Applying JD method with transmission limit constraint: Here, proposed JD method with transmission limit is applied on the IEEE 30-bus system. The results of applying this method are shown in Fig. 6. According to Table 3, maximum capacity of lines 9-11 and 12-13 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.

Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint
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
Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint

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, Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint is power flow from bus i to bus j only for energy production, Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint is power flow from bus i to bus j for sum of energy and SR and Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint 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 9-11 and 12-13. Also when they want to produce their allocated SR, overload is happened in lines of 12-15, 15-18 and 15-23 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
Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint

Table 9: DC power flow results for 19 h considering energy and SR pattern via JD method with transmission limit
Image for - Dynamical Joint Energy and Spinning Reserve Dispatch Considering 
        Transmission Network Constraint

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 GA-based 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.

REFERENCES
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