Spinning Reserve Opportunity Cost in Hydroelectric Plants T. Sousa, Student Member, IEEE, J. A. Jardini, Fellow, IEEE, M. Masuda, and R. A. de Lima
Abstract – Starting from the deregulated process of the Electric Sector, there was the need to attribute responsibilities to several agents and to elaborate appropriate forms of remuneration of the services rendered by the same. One of the services of great importance within this new electric sector is the Ancillary Services. Among the various types of Ancillary Services, Spinning Reserve is a service necessary for maintaining the integrity of the transmission system from either generation interruptions or load variations. This paper uses the application of the Economic Dispatch theory with the objective of quantifies the availability of Spinning Reserve supply in hydroelectric plants. The proposed methodology utilizes the generating units as well as their efficiencies so as to attend the total demand with the minimum water discharge. The proposed methodology was tested through the data provided by the Água Vermelha Hydroelectric Power Plant. These tests permitted the opportunity cost valuation to the Spinning Reserve supply in hydroelectric plants. Keywords – Ancillary Services, Opportunity Cost, Spinning Reserve.
Hydraulic
Generation,
I. INTRODUCTION The deregulation of the electric sector is a new topic throughout the world and the transition from a regulated environment to a competitive market imposes a distribution in the operational costs, in a way that the agents involved receive adequate payment and the requirements are fulfilled, thus, making market transactions feasible. With the need of partitioning operational costs it also came up the need of discretizing the different types of services. This, with the objective of understanding and organizing them according to their function and define methodologies to identify both service providers and service users. Within the unbundled electric sector, focus has been put on the class of services that contribute to the security, reliability and quality of power supply. Such services are referred to as Ancillary Services. Among the Ancillary Services, spinning reserve or active power reserve, is a service that is necessary to maintain the integrity of the transmission system under the presence of events and disturbances (contingencies). The need of active power reserve arises from various causes, although This work was supported by the AES Tietê S.A.. T. Sousa, J. A. Jardini and M. Masuda are with the Department of Electrical Engineering, Sao Paulo University, Sao Paulo, BR (e-mail:
[email protected]). R. A. de Lima is with AES Tietê S. A., Sao Paulo, BR (e-mail:
[email protected]).
the two more important, are: generation interruptions and load variations. Sustained energy instabilities are not permitted for they may eventually lead to system failure, drop (or increase) of frequency, thus, resulting in uncontrollable interruptions. Due to the importance of making active power reserve available to the system, several papers have been published the objective of optimizing the provision of this service so as to attend the restrictions imposed by the Electric System [1][6]. This paper proposes a methodology for the dispatch of the machine, based on the use of the Economic Dispatch theory. The proposed methodology uses the efficiency of the turbines and minimizes the water flow of the hydroelectric plant, reducing costs related to the system efficiency and so attend the operative restrictions of such power plants. Some tests using data provided by the Água Vermelha Hydroelectric Power Plant were realized. The tests carried out showed good results and permitted the opportunity cost valuation in the Spinning Reserve supply. The analysis corresponding to the year 2002. The present work is organized as follows: Section II, presents the various costs associated to the supply of reactive power reserve. Section III, presents a summary on the calculation of the hydro generators efficiency. Section IV, presents the formulation of the Economic Dispatch approach and the technique used for the solution of the problem. Section V presents the tests and results obtained through the proposed methodology. In the last section, the conclusions of the paper are presented. II. ASSOCIATED COSTS TO THE AVAILABILITY OF ACTIVE POWER RESERVE In this section, the costs associated with the spinning or stand-by power reserve supply for hydro systems will be presented [7]. A. Investment Costs Investment costs consist of capacity cost and also the control cost for the equipment and other items necessary for the service. Equipment control cost is small when compared to the total capacity cost and the equipment is usually installed independently of the Ancillary Service functions, because most of the equipment is necessary to initiate and synchronize a unit. A gross estimation indicated that
equipment that is necessary to make active power reserve available is approximately 2% of the total investment. B. Operational Costs to Maintain the Control Function on Stand-by The cost for having control over the quick reserve in the generation system is affected by how the efficiency of the generator depends on the output. The efficiency curves of hydraulic units depend on the type of turbine used. It commonly occurs in these curves that the maximum efficiency is below the maximum output generation. For example, a Francis turbine is generally projected to have its maximum efficiency at 80% of the maximum output. This means that when the units operate at its utmost efficiency, which is necessary in normal operations, there is enough quick reserve available with no additional costs. The operational cost to maintain the stand-by reserve includes, generally, the cost of employees and other operational costs to maintain the available aggregate to star-up the machine in 15 minutes. These costs are low when compared to the total investment. C. Operational Costs to Activate the Reserve These costs consist of costs related to the efficiency generated by the most efficient shunting levels and can also include start-up costs, when there is a need to involve extra units. The cost related to the efficiency can be high, that is because the reduction in efficiency affects the entire production of a specific unit and not only the additional production that is necessary to represent the reserve control. Units having flat efficiency curves are used for active power reserve services. It is reasonable to estimate an efficiency reduction in the order of 3%, if the output is increased by 20% above the best efficiency level. If this reduction in efficiency, which affects the entire production, is loaded by the added 20%, which comes as an addition, an increase in costs of this 20% will appear in the 15% related to ordinary production. This is a gross estimation of the marginal cost, but it provides a certain indication of the level. Start-up costs, when the reserve is on warm stand-by, may also be included here, which is the case of secondary control reserves. These costs are caused by the wear out (cavitation) of the turbines and by a certain amount of wasted water, which is translated into a fixed cost component and a variable cost component, that is, wasted KWh multiplied by the market price. This paper uses the efficiency characteristics of the turbine/generator set to optimize the active power of the spinning reserve service. III. EFFICIENCY OF THE TURBINE/GENERATOR SET To analyze the active power of the spinning reserve, the efficiency characteristics of the turbine/generator set, will be used. The efficiency η refers to the combined efficiency of both the turbine and the generator. The efficiency can be modeled in different ways, depending on the available data and on the desired accuracy provided by the hydroelectric
power plant model. For long-term studies, with monthly discretization intervals, a constant value of η is usually adopted, and it is equal to an average efficiency. Models regarding the operation of a power plant in shorter discretization intervals, such as days, hours or real time, should consider the variations of η linked to the turbine operating conditions. The term “Operating conditions” includes the net head, the water discharge (flow) and the power generated. The relation among these variables is complex and it is usually modeled through the turbine performance curves. The equation of the power generated by the power plant, is presented in (1).
p( t ) = η ⋅ ρ ⋅ g ⋅ h ⋅ q( t ) ⋅ 10 l
6
(1)
Where, p(t) is the power generated (MW); g is the gravitational acceleration (m/s2); ρ is the specific weight of water (kg/m3); η is the efficiency of the turbine/generator set (%); hl is the effective water head (m); q(t) is the plant’s water discharge (m3/s). Fig. 1 presents the performance curve of a Francis type turbine [8]. The generating units of the power plant used in this paper are Francis turbines. Note in Fig. 1, that there is a point where the efficiency is at its maximum, called Project Point. Due to the definitions of reference values used to express percentages of power and effective head, the project point is the point in which power and effective head are both equal to 100%. In all other turbine operation conditions, the efficiency will be less than that of the Project Point. This does not mean that the power generated by the turbine at the Project Point, will be the maximum. For example, at the Project Point the opening of the blades is 92%; if the effective head is maintained constant and the blades continue to be 100% open, the power generated by the turbine will increase and reach 123%. However, the efficiency associated with this point will be less than that of the Project Point. This means that with the effective head at 100%, the turbine uses up more water per MW produced when it generates 123% than when it generates 100% of power. From Fig. 1, it can also be observed that for the same opening of the turbine blades, as the effective head is increased, the power generated also increases. This occurs because of two factors. Firstly, the power generated is proportional to the effective head; therefore, if the effective head is increased, the power generated will also increase. Secondly, as the effective head increases and the blades are kept with the same opening, due to the increase in pressure, so the water flow through the turbine will do. Since the power generated is also proportional to the flow of the plant, the power generated increases.
Next, the formulation of the Economic Dispatch problem utilized in the optimization of the active power reserve will be presented.
Fig. 1. Performance curves for a Francis type turbine.
The second effect explains why the increment rates of the power generated due to the increase in effective head is different for different openings. For example, for a 20% opening, the power generated varies from 14% to 23% when the effective head varies from 80% to 100%. Now, for an opening of 100%, considering the same variation in the effective head, the power generated varies from 77% to 123%. Since the variations in the effective head are the same, it is concluded that the increase in the power variation is caused by the increase of the water flow plant. Figures 2 and 3, can also be used to explain some characteristics of the turbine. Considering a fixed effective head, and as the blade opening progressively varies from 20% to 100%, the water flow through the turbine increases, thus, increasing the generated power. This occurs because power is basically determined by the product between effective head and the water discharge of the plant [9]. Since the effective head is considered constant, as the blades are opened, the water flow increases and the power generated rises.
Fig. 3. Turbine efficiency for different heads.
IV. PROBLEM FORMULATION The optimization of the active power reserve can be seen as an Economic Dispatch problem, as presented in this section, although the water discharge of the plant becomes the objective function to be minimized.
Min FT = Min ∑ F ( Pi ) T
(2)
i =1
s .t .
∑ Pi − Pd i =1 T
=0
Pmin < Pi < Pmax Pi ∈ N
(3)
L ,T
i = 1,
(4) (5 )
Where: FT is the objective function to be minimized. For the proposed problem this function is represented by the plant’s water flow in relation to the active power generated (Pi); Pi is active power generated by the ith unit; Pd is total active power required by the power plant; Pmin and Pmax are the minimum and maximum limits of generation, respectively; T is the number of units; N is a real number.
Fig. 2. Power generated by turbine for different net heads.
As for the turbine efficiency, it presents a different behavior. At the beginning, when the blades begin to open, the efficiency progressively increases, thus reaching the point of maximum output for a specified effective head. Thereby, the efficiency decreases with the increase of the opening.
With the minimization of the water discharge there is an improvement in the efficiency of a generating unit for a determined generation of active power. As previously described, when units operate at their best efficiency, which is necessary in normal operations, there is enough quick reserve available with no additional costs. This point of operation is defined as the point of minimum fuel consumption for a maximum power generation. The obtention of this operation point makes possible to reach optimized active power reserve.
intervals of the values contained in the database used (between 90 and 240 MW). Observe in Fig. 4, that for water discharge intervals contained in the database the approximation to a seconddegree function results in a curve that is quite similar to the T T measured curve. L( Pi , λ , µ ) = FT + λ i ( Pi − Pd ) + µ 1i ( Pi − Pmax ) From the approximation got in the measured curve, i =1 i =1 through a second degree function and based on the T + µ 2 i ( Pmin − Pi ) (6 ) optimization theory presented, it can be concluded that for the i =1 same number of machines (considering them similar), the best operative rule is that they all should be generating the same The optimizing conditions, taking into account a general active power. problem, for points xo, λo, µo, are given by:
The optimal solution for the problem (2)-(4) can be obtained by using Lagrangian techniques and using the Karush-Kuhn-Tucker (KKT) conditions [10]. The Lagrange function for the proposed problem is presented next.
∑
∑
∑
∂L o o o ( x ,λ , µ ) = 0 ∂Pi wi ( x o ) = 0 gi ( x o ) ≤ 0
µ gi ( x ) = 0 ⎫ ⎬ µi0 ≥ 0 ⎭ 0 i
o
K to i = 1,K , Nw ( 8 ) to i = 1,K , N ( 9 ) to i = 1,K , N ( 10 ) to i = 1, , N ( 7 )
g
g
Where: Nw is the number of equality equations and Ng is the number of inequality equations for the given problem. For a condition where the generating units are identical, the total power generated must be equally distributed among the units in operation, so as to minimize the water flow of the plant, thus, optimizing the active power reserve [10]. When the generation units are different, the generation of active power is distributed among the units using the conventional Economic Dispatch problem, as it is used for thermal units. V. TESTS AND RESULTS With the objective of evaluating the turbine/generator set and thereafter valorize the active power reserve supplied by the generating units, data from the Agua Vermelha Hydroelectric Plant will be used in the tests. This plant forms part of the AES Tietê group. The base year used in the tests was 2002, which has the data available for each day, hour by hour, with the number of machines utilized along with the power dispatched according to what was determined by the System Operator. In this paper, four different tests were realized. The first one considered that all the machines at the Água Vermelha Hydroelectric Power Plant would be working with the same generation, so as to attend the total demand. The objective of this test was to quantify the amount of MW that would be saved, if this operational characteristic was used. To this end, an approximation curve of water flow vs. generated active power available for a second-degree function was made. This approximation enabled to estimate the water discharge necessary to generate power (MW) that would be outside the
Fig. 4. Water discharge curve (m3/s – y axis) in relation to the active power generated (MW – x axis).
After determining the function that represented the curve, the next step was to determine the water discharge used to generate the power measured in the machines in the year 2002, and determine the water flow that would be used in case the machines may be operated with the same generation. Once determined the water discharges, it was calculated the differences between these values, thereafter, the water discharge difference was converted into MW. The base power was that in which each machine would be generating, if the operational policies were that in which all of them would be generating the same power. The difference found was referred to as Power Economy. The value of the Power Economy found for the described test was of 7.853 MWh for the base year. This was followed by a second test that measured the Power Economy in case the power plant considered the option of attending the demand, though being free of disconnecting a machine (N-1 machines). Yet, maintaining all the machines with the same power generated. Some conditions were adopted for the realization of this test: • If during the hour of analysis, the Hydroelectric Power Plant would be operating with only 2 machines, the choice would be to continue operating with only 2 machines both with the same generation; • In case the power generated by each machine (if N-1 machines are being used) surpasses its maximum generation value, the choice was to continue the operation with the initial number of machines, all with the same generation;
• In case the choice of using N-1 machines did not result in any benefit (i.e. a Power Economy), the choice made was to continue the operation as in the beginning; • Otherwise, it was chosen the option to attend the demand with N-1 machines, all generating with the same power. After fulfilling all these conditions, it was determined both the water discharge used to generate the power measured in the machines, and the water discharge that would be used to comply with the conditions imposed. Once determined these discharges, the difference between these two values was calculated and converted into MW. The Power Economy found for this test was 43.625 MWh in the base year. This value corresponds to 0.77% of the total Água Vermelha Hydroelectric Power Plant generation, for the year of 2002. As previously stated, the necessary water flow to generate a power that would be outside the interval contained in the database (90 a 240 MW) was estimated through the seconddegree function obtained. Such estimation may result in some errors in the Power Economy obtained. With the aim of avoiding such errors, it was proposed a third and a fourth tests. The third and fourth tests are basically similar to the first and second tests respectively. The difference laying in the fact that the water discharges previously estimated, through the second-degree equation, would now be obtained taking into consideration that the efficiency of the machines operating with a power less than 90MW, are equal to the efficiency of the machines operating with 90MW. It should be pointed out that the efficiency information for the adjustment of the curve does not contain values for a power less than 90MW, and that the extrapolation may introduce an error. The Power Economy found for the third test was 3.548 MWh for the base year. The Power Economy for the fourth test was 35.555 MWh (base year). This Power Economy obtained corresponds to 0.62% of the total generation at the Água Vermelha Hydroelectric Power Plant (year 2002). Fig. 5 shows the results of the referred tests. Fig. 5a illustrates the representative curve of the relation between the water discharge (Q) and the power generated (P), that is, Q/P (y axis) and power generated (x axis). The small circles shown represent the generation points at a given time. It can be observed that, there are generations with less than 90MW. For these points, it was assumed the same Q/P relation used to generate 90MW. This was the main difference between the third and fourth test. Fig. 5b illustrates the curves obtained for the Q/P relation (y axis) from the database with the generated power (x axis) as well as the curve obtained for a second-degree function originated from the regression of the points contained in the database (relation between the water flow and the power generated). Fig. 5b shows the similarity between these two curves. Fig. 5c illustrates the curves obtained for the water discharge (y axis) from the database and power generated (x
axis) as well as the curve obtained for a second-degree function originated in the regression of the points contained in the database of the water discharge and the power generated. Fig. 5c shows the similarity between these two curves. Fig. 5d, shows the curve obtained for the relation of the water discharge (y axis) and the power generated (x axis), from the database. The points illustrated correspond to the water discharge data for a certain generation power at a given time. It can be observed that for generations below 90MW, the water flow values are proportional to the 90MW generation relation. VI. CONCLUSIONS From the theory described previously, it can be concluded that most of the costs associated to the supply of active power reserve come from the costs related to the efficiency of the turbine/generator set. Thus, this paper has presented a methodology to determine the dispatch of the generation units so as to optimize the active power reserve service, starting from the maximization of the generating units efficiency. Based on the proposed alternatives and their solutions, it can be observed that the savings attained with the optimization of the active power reserve could be in the order of U$ 0.87 millions a year, in case of considering a MWh equivalent to U$ 20.00 (Twenty dollars). These monetary values are based on the Power Economy presented in the tests realized. This results measure the opportunity cost if the proposed alternatives was employed. In case the System Operator requests to the generating agents to operate under a configuration where the generating units need to operate at points distant from the maximum efficiency, it would be important to provide a compensation to the generating units for services rendered. This is because the generating unit is consuming a greater quantity of fuel that would actually be necessary to attend the demand, disregarding the expenditures related to personnel and maintenance. In case the generating units would not be operating at their best efficiency, without being requested to operate by the System Operator, it is necessary that the generating agent could correct its dispatch operation, so that to avoid fuel waste which may imply a loss in its budget. VII. REFERENCES [1]
O. Nilsson, L. Söder, and D. Sjelvgren, "Integer Modelling of Spinning Reserve in Short Term Scheduling of Hydro Systems," IEEE Trans. Power Delivery, vol. 13, pp. 959-964, Aug. 1988. [2] A. Schmitt and J. F. Verstege, "A Multi-Criteria Optimization of Ancillary Services with Pareto-based Evolution Strategies," in Proc. 2001 IEEE Porto Power Tech Conference. [3] A. Arce, T. Ohishi and S. Soares, "Optimal Dispatch of Generating Units of the Itaipú Hydroelectric Plant," IEEE Trans. Power Delivery, vol. 17, pp. 154-158, Feb. 2002. [4] X. Guan, Q. Zhai, and A. Papalexopoulos, "Optimization Based Methods for Unit Commitment: Lagrangian Relaxation versus General Mixed Integer Programming," in Proc. 2003 IEEE Power Engineering Society General Meeting, vol. 2, pp. 1095-1100, July.
[5]
N. P. Padhy, "Unit Commitment Problem Under Deregulated Environment – A Review," in Proc. 2003 IEEE Power Engineering Society General Meeting, pp. 1088-1094. [6] H. Y. Yamind, "Review on Methods of Generation Scheduling in Electric Power Systems," Electric Power Systems Research, no. 69, pp. 227-248, 2004. [7] F. L. Alvarado (Convenor), "Methods and Tools for Costing Ancillary Services, " Cigré - Task Force, no 190, June 2001. [8] L. A. M. Fortunato, T. D. A. Neto; J. C. R. D. Albuquerque, and M. V. F. Pereira, "Planning and Operation of Electric Power Systems Introduction," EDUFF – Ed. Universitária, p.p. 232. (in portuguese). [9] D. S. Filho, "Uma Nova Abordagem ao Dimensionamento EletroEnergético de Usinas Hidroelétricas para o Planejamento da Expansão da Geração," PhD. Thesis, Engineering School of Sao Carlos, University of Sao Paulo, Sao Carlos. (in portuguese).
[10] A. J. Wood, and B. F. Wollenberg, "Power Generation, Operation and Control", 1984.
Fig. 5. Tests considering that the efficiency of the machines that operate with power below 90MW is the same to the efficiency of the machines operating with 90MW.
VIII. BIBLIOGRAPHIES Thales Sousa was born on June 23, 1978. He received his B.Sc. degree from the Sao Paulo State University (UNESP) in 2000. He obtained his M.Sc. degree at the University of Sao Paulo (USP) in 2003. Currently, he works as a researcher at GAGTD in the Polytechnic School at the University of Sao Paulo. He is working for his PhD. degree in the Department of Electrical Engineering of the latter institution. His research interests are power system operation and planning. José Antonio Jardini, was born on March 27, 1941. He received his B.Sc. degree from the Polytechnic School at the University of Sao Paulo (USP) in 1963. Subsequently, he obtained his M.Sc. and Ph.D. degrees in 1970 and 1973, respectively, all from the same institution. From 1964 to 1991 he worked at Themag Eng. Ltd in the area of Power Systems & Automation and Transmission Lines projects. Currently, he is a Professor in the Department of Engineering of Energy and Electric Automation at USP. He is a member of CIGRE and was the Brazilian representative in the SC38 of CIGRE, Fellow Member of IEEE and Distinguished Lecturer of IAS/IEEE. Prof. Jardini’s fields of interest are: Generation Automation, Transmission and Power Distribution. Mario Masuda, was born on June 25, 1948. He received his B.Sc. degree in Electrical Engineering from the Polytechnic School at the University of Sao Paulo, in 1973. From 1973 to 1991, he was with Themag Eng. Ltda working in the area of Power Systems & Automation and Transmission Lines projects. From 1991 to 1997, he worked independently executing projects, supervising and teaching courses related to the installation of fiber optic cables in transmission lines (OPGW). From 1997 to 2002, he worked at Furukawa and Constructions Ltd., with the lastly mentioned activities. Presently, he works as a researcher at GAGTD in the Polytechnic School at the University of Sao Paulo.
Rodrigo Alves de Lima was born on January 07, 1980. He received his B.Sc. degree in Electrical Engineering from the State University of Sao Paulo (UNESP) with emphasis in power systems. Currently, he works at AES Tietê S.A, in the field of regulation.
