ECONOMIC LOAD DISPATCH FOR A POWER SYSTEM WITH RENEWABLE ENERGY USING DIRECT SEARCH METHOD Warsono, D. J. King, and C. S. Özveren University of Abertay Dundee, Scotland, UK
ABSTRACT The inclusion of a significant amount of renewable energy into power systems, which is set to increase significantly in the near future, has resulted in additional constraints on Economic Load Dispatch (ELD) such as more unpredictable ramp rate and the need for additional reserves to accommodate the intermittent nature of the output. This condition may not match with the system load demand in a power system. A Direct Search Method (DSM) using ‘negative load’ and ‘inclusive’ approaches to ELD, which takes account of the variable wind generation, is proposed and discussed and compared with previously reported Genetic Algorithm (GA) method. Keywords: Economic Load Dispatch (ELD), Direct Search Method (DSM), renewable energy, wind power generation. 1. INTRODUCTION The use of renewable energy for electricity generation will increase in the future due to environmental pressures, particularly those regarding global warming. Consequently, the role of renewable energy will become more significant in the operation of electrical systems. The difficulties with renewable energy are the continuity and reliability problems associated with its operation. The output of some renewable generation, such as wind and wave generators, is determined by the climate and weather conditions and operating patterns will therefore follow these natural conditions. These patterns may not match the system load profile. Therefore, it is clear that the problem of how to integrate renewables within power systems needs special consideration and will require new methods for allocating its output. Wind energy is the fastest growing renewable energy source because of its abundance in nature and the maturity of its technology. In 2002 the European Wind Energy Association (EWEA) estimated the use of wind turbines in the UE-15 to be 5.5% of total energy and predicted that it would increase to more than 12% by 2020 [1]. Bio-diesel is another emerging renewable energy source, which is able to act as a replacement for oil [2]. The attractive property of bio-diesel is that it is easily stored and can be used by fast ramp rate engines, such as diesel engines. Bio-diesel may potentially be used as a back-up source to compensate for the unpredictability of renewable energy. The paper will focus on the short-term dispatch of renewable sources in a power system. As indicated, the
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main problem faced by these sources is the intermittent nature of its output, which often does not suit the load demand profile. The problem regarding the impact of renewable energy on power system operation has been discussed in several papers. Denny and O’Malley [3] discuss the effect of wind generation on power system operation and emission reduction. Another study from Ummels [4] also assesses the impact of wind energy on thermal generation unit commitment and dispatch based on the Dutch system which has a large amount of combined heat and power (CHP), and concludes that due to this there are no ramp rate problems regarding wind penetration. The other important issue of wind energy on the power system is its effect on reserve requirement. Based on the case of the power system in Ireland, Doherty [5] asserts that a high installed capacity of wind energy causes an increase of reserve requirements due to wind forecasting error. Dani [6] also investigates the impact of wind energy on the increasing need for reserve requirements. He suggests the need for both “positive” reserves for compensating power deficits and “negative” reserve for avoiding power surpluses. Doherty [7] shows that the increase of the forecast time horizon will also increase reserve requirement due to the increase of the standard deviation of the total wind power forecast. Doherty [5] identifies two scenarios for dispatching wind turbines in the power system. The first is the fuel saver scenario that does not consider forecasted wind power in the load dispatch mix. In real time operation, when wind power output is present, conventional generators will reduce their output in merit order so that it can be accomodated. If wind power output increases such that it cannot be integrated by reducing conventional
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generation, then wind production will be curtailed. There will be wasted wind output. The second scenario is the forecasted approach. In this scenario, wind power forecasts are included in the Economic Load Dispatch (ELD) calculation. The forecasted approach should consider the increase in reserve requirement due to wind forecast error. Therefore, reserve constraints in the ELD when there are large amounts of wind power will become more complex. Therefore, wind forecasting will also be an important part of the ELD problem. Consequently, a more flexible and powerful method that can cope with the extra constraints caused by wind penetration should be used to solve the ELD problem. A study using a Genetic Algorithm (GA) method for this case has been demonstrated by the author [8]. In this paper a Direct Search Method (DSM) will be investigate for comparison with the GA method. The DSM is a simple and effective method for solving optimisation problems that does not required any information about the higher derivative of the objective function. It only uses objective function values to search for an optimal solution. Therefore, DSM has the potential to solve non-continuous, non-smooth, and nondifferentiable optimisation problems [9] and has been reported as an effective method for solving some cases of the ELD problem in power systems with specific constraints, such as transmission capacity [10] and valvepoint effects [11]. The paper will investigate a DSM for solving the ELD problem to minimise cost for generators in power systems that contain renewable energy using the simulation model developed by author in the previous paper [8]. 2. PROBLEM FORMULATION This paper reports on initial investigations of the topic; therefore some simplifications have been made. 2.1 Dispatch Model Generators in the system consist of thermal, wind and diesel. Fuel for diesel generators is assumed to be biodiesel. Constraints included in the calculation are the maximum and minimum values of generator output, the ramp rate of the generators, and reserve requirements. For simplification, transmission losses are neglected. The economic dispatch process aims at cost minimization subject to these constraints. The solution flowchart is shown in Figure 1. This paper will use as a basis the ELD models suggested by Doherty [5]. Initially, a no wind scenario is used as a base case and then a forecasted scenario is also applied. In the forecasted scenario, two approaches to deal with wind generators will be applied as follows:
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Figure 1. Flow chart of ELD problem 2.1.1. ‘Negative load’ approach In this approach the wind forecast is treated as a ‘negative load’. Therefore, load demand is reduced by the forecasted wind power, producing a new load demand. This new load demand is then used in the ELD process. 2.1.2. ‘Inclusive’ approach In this approach, wind turbines are included in the calculation. In order to reduce emission, wind output should be used as much as possible. Therefore this method maximise the use of wind power on the system. The objective function of the ELD is formulated as follows: Min ( ΣCpi Pi + ΣCri Ri), i=1,2,..., Subject to constraints: Pload - Σ Pi = 0, Pimin Pi Pimax DRi.∆t Pit+1 - Pit , for Pit+1 < Pit URi.∆t Pit+1 - Pit , for Pit+1 > Pit , Σ Ri Rmin Where: i,N
(1)
(2) (3) t=1,2,...,T (4) (5)
= generator number, and total number of generators t, ∆t, T = time (in hours), increment of time and maximum time horizon, respectively Ci, Cri = the cost of power output and reserve of generation i Pi, Ri = power output and reserve of generation i Pload = Load demand Pimin,Pimax = minimum and maximum output of generator i DRi, URi = the down ramp and up ramp limit of generator i, respectively Rmin = Minimum reserve requirement
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2.2. Generation Cost Model 2.2.1 Thermal Generators It is assumed that each generator has a four-step incremental cost curve. The curves of operating and incremental costs are shown in Figure 2.a and 2.b, derived and modified from Wood and Wollenberg [12]. The cost data and operating limit of each generator are shown in Table 1 and 2, respectively.
Figure 3. Wind generator characteristic function 2.2.3. Bio-Diesel Generators Total capacity of all bio-diesel generators is 150 MW and the cost characteristic (Cd) is assumed to be a simple linear function of generator output (Pd). Cd = 80 Pd
(b)
(a)
Figure 2.Thermal generator cost characteristic (a) The incremental cost curve, (b) The cost curve Table 1. Thermal generator cost at various ranges P1
$/MW
P2
100 200 300 400
12 20 28 36
75 125 175 225
$/ MW 25 29 33 35
P3
125 250 375 500
$/ MW 22 26 30 35
$/ MW 16 25 31 40
P4
75 175 225 300
Table 2. Operating limit and ramp limit of thermal generators Unit P1 P2 P3 P4
Pmax
Pmin
400 225 500 300
75 50 100 50
UR
70 90 100 60
-95 -110 -135 -75
(6)
Where, Nw is the number of wind turbines and Pw is the power output of the individual wind turbine, which is itself a function of the wind speed, w. A typical characteristic of wind output [13] as a function of wind speed is used in this paper. The curve characteristic and appropriate data for the wind generators are shown in Figure 3. The total capacity of the wind turbines is 180 MW, with cut-in, full capacity and cut-off speeds of 3 m/s, 13 m/s and 25 m/s, respectively. The wind cost (Cw) has a high capital cost and low operational cost and is assumed to be as follows: Cw = 3082 + 0.1 Pwt
2.3. System Operation Scenario In order to satisfy demand and other constraints all thermal generators are considered to be committed. All forecasted wind output should be fully utilised to minimise fuel consumption and reduce emissions. Bio-diesel generators are committed when the reserve requirements are not fulfilled by thermal reserves. Reserve requirements are based on the next hour availability, therefore the maximum reserve provided by thermal generators is limited by the up ramp limit (UR). All bio-diesel generators have a sufficiently fast ramp rate. 2.4. Reserve Requirements Due to the uncertainty of wind output, reserve should be increased to take this into account [5, 6]. The additional reserve will also rise with the increase of the time horizon [7].
DR
2.2.2. Wind Generator The wind source consists of a number of wind turbines. For simplicity, all wind turbines are considered to be identical. Therefore, the total wind power output, Pwt, is: Pwt = Nw.Pw(w)
(8)
For simplicity, the normal reserves (Rn) are based on load demand, and additional reserves (Ra) due to wind power are based on wind output and time horizon, which is derived from the graph of typical standard deviation by Doherty and O’Malley [7]. Therefore: Rn = 0.25Pload
(9)
R = xPwt
(10)
Where, x is 0.20 for t=1, 0.225 for t=2, 0.24 for t=3, 0.25 for t=4, 0.26 for t=5, and 0.27 for t=6 and above. The reserve cost for generator P1, P2, P3 and P4 are $1/MW, $2/MW $1.5/MW and $1.75/MW, respectively. 2.5. Load Demand and Wind Power Forecast In the simulation, load and wind power forecast are carried out for a 12 hour period with peak load derived from a typical peak load pattern in Indonesia. Wind power is derived from the wind speed forecast using the wind generators characteristic function of Figure 3.
(7)
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In the absence of typical wind profiles, in order to test the approach a profile based on a randomized sinusoidal has been used to represent its fluctuation and uncertainty. The load demand and wind power forecast are shown in Figure 4. 1400
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Figure 4. Load demand and wind power forecast 2.6. Direct Search Method A DSM is simply structured to search a set of points, around a current position, looking for a point with a smaller objective value than that of the current position. [11]. A Pattern Search (PS) is one of most common techniques of DSM, which is simple and suitable for solving a variety of optimisation problems [9]. Basically, the PS algorithm evaluates a sequence of points that converge to an optimal point. The algorithm begins by searching a set of points called a mesh, around the starting point determined by the user. The mesh is formed by adding a scalar multiple of a set vector called a pattern to the starting point . When a new point in the mesh provides the lowest objective value, the new point becomes the new starting point at the next iteration.
The algorithm is repeated as illustrated above until convergence occurs. Examples of convergence criteria are: The mesh size is less than a pre-set mesh tolerance The number of iterations reaches a predefined value The distance between the point found at one successful poll and that of the next successful poll is less than a set tolerance The change of the objective value from one poll to the next poll is less than the tolerance value. 3. RESULTS AND DISCUSSION The calculations for three simulations were done using MATLAB. The results are presented as follows. 3.1. Results 3.1.1. No wind case As a base case, the results of calculation for system without wind power are shown in Figures 6.a and 6.b.
As an example, a two variable optimisation is shown where Xo is the starting point chosen by the user. At the first iteration, with the mesh size of 1, the PS algorithm constructs a pattern vector or a direction vector, with the value of [1 0], [0 1], [-1 0], and [0 -1]. Then the direction vector is added to Xo, producing mesh points, which are Xo + [1 0], Xo + [0 1], Xo + [-1 0] , and Xo + [0 -1]. These points can be seen in Figure 5.
MW
Wind(MW)
100
Load (MW)
1000
120
The point is set as a new starting point (X1) for next iteration. After a successful poll, in the next iteration the mesh size is multiplied by 2 (for example), which is called the expansion factor. Therefore, the mesh points at 2nd iteration are: X1+ 2*[1 0], X1+ 2*[0 1], X1+ 2*[-1 0], and X1+ 2*[0 -1]. The poll is performed again, and if it is successful, another starting point (X2) is set. In the 3rd iteration, the mesh size becomes 4, because the expansion factor is 2. When the poll is unsuccessful or is unable to provide a smaller objective value, the current point is then left unchanged and in the next iteration the mesh size is contracted, for instance by a factor of 0.5.
500 450 400 P1
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150 100 50 0 1
MW
+
Xo
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hours
10 11 12
Figure 6. A. Generation mix from no wind case
Xo+[0 1]
Xo+[-1 0]
2
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350 300 250
Xo+[0 -1]
Rd 200 R4 150
Figure 5. The starting point and the mesh points The mesh points are then polled by computing their objective function values, if one of the mesh points produces a better value it means the poll is successful.
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R3
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Figure 6.b. Reserve composition of no wind case
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3.1.2. The ‘negative load’ approach In this approach, wind power is treated as negative load. The results are shown in Figures 7a.and 7.b. 450 400 350 300
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P4
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Pw
100 50 0 1
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10 11 12
hours
Figure 7. A. Generation mix from ‘negative load’ approach MW
3.2. Discussion It is shown that the system can overcome the variability of the wind output in the above power system. The inclusion of wind power in ELD calculation, in this case, has impacts on the generation mix, cost, variability of load seen by other plants, and reserve requirement. The impact on the generation mix can be seen in Figure 6.a, 7.a, and 8.a.
350 300 Rd
250
R4
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R3
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R2
By using DSM, the generation mix resulting from ‘negative load’ and ‘inclusive’ are different. In the previous simulation using GA method the same generation mixes resulted from both methods [8]. Besides, the results of DSM for solving ‘inclusive’ approach are not reliable, because when the simulation is repeated the result will be different, as shown in Table 4 columns 3 and 4. Therefore, the result of ‘inclusive’ approach is not included in the next discussion. Table 4. The Comparison of the Result of Calculation .
R1
Generator P1 P2 P3 P4 Pw Total
100 50 0 1
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hour
12
Figure 7. B. Reserve composition from ‘negative load’ approach
MW
3.1.3. The ‘inclusive’ approach In this approach, wind generators are included in the calculation. The results are in Figures 8.a. and 8.b. 450 400 350 300
Neg Load 200 75 125 96 65 561
Inclusive 1 171 56 194 75 65 561
The cost result comparison of all approaches in this case is shown in Figure 9. In general, the ‘negative load’ approach reduces the system costs. But the reduction in cost is not real, because wind cost is excluded in the calculation. Nevertheless, in hour 7 when additional biodiesel engines are added for compensating high load ramp and additional reserves, the cost is still higher than in the ‘no wind’ case
P1 P2
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10 11 12 hour s
Figure 8.a. Generation Mix of ‘Inclusive’ Approach
10000 5000 0 1
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No Wind MW
Inclusive 2 142 75 176 103 65 561
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Neg Load
Figure 9. Cost comparison
350 300 250 Rd R4 R3 R2 R1
200 150 100 50 0 1
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Figure 8.b. Reserve from ‘Inclusive’ approach
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The impact on variability is reflected in load ramp seen by other plants which becomes more unpredictable compared to when there is no renewable energy. The reserve requirement needed by the system with wind power is increased. In this case, the increase of the reserve varies from 9 MW to 43 MW or from 3.68% to 22.8%, with the average of 25 MW or 11.6%. This shows that the role of additional bio-diesel plants as back up is very important.
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The convergence and the mesh size for ‘negative load’ approach are shown in Figure 10.
Figure 10. The convergence and mesh size curve of ‘negative load’ approach. 4. CONCLUSION As there will be an increasing use of renewable energy in the future, it is important to study its impact on the operation of power systems and in particular the ELD problem. This paper reports an initial study focusing on the use of the DSM for ELD with renewables. Several basic models dealing with the problem of ELD are implemented for a simple case. It has been demonstrated that the inclusion of renewable energy in the power system in this case has impacts on generation mix, cost, the variability of load seen by other plant, and reserves. The results presented provide an initial verification of the hypothesis that to compensate for the variability of renewable energy, the ramp rate capability of the plant plays an important role and that fast ramp rate plant such as bio-diesel engines can be used to compensate for this variability. The DSM can cope with the problem well in the ‘no wind’ case and the ‘inclusive’ approach, but it is unable to present reliable results in the ‘inclusive’ approach. Unlike the GA method which gave consistent results for both cases. Because wind power cost is assumed to be zero for ‘negative load’ approach, the result does not reflect the real cost. Therefore, the actual wind power costs should be added in the ‘negative load’ approach.
2. Gerpen, J.V., Business Management for Biodiesel Producers. National renewable energy laboratory, Colorado. 2004 [online] Available from http://www.nrel.gov 3. Deny, E., O’Malley, M., Wind generation, power system operation, and emission reduction. IEEE Trans. on Power System. Vol. 21. p. 341-347, Feb 2006. 4. Ummels, B.C. et al, Impacts of Wind Power on thermal generation unit commitment and dispatch, IEEE Trans. On Energy Conversion, Vol. 22, March 2007 5. Doherty, R. et al, Sistem Operation with a Significant Wind Power Penetration, IEEE Trans. Power System. Vol. 20. pp. 587-595, May 2005. 6. Dany, G. Power reserve in interconnected systems with high wind power production, IEEE Porto Power Tech Proceedings, Vol. 4, Sept. 2001 7. Doherty, R. et al, A New Approach to Quantify Reserve Demand in Systems With Significant Installed Wind Capacity, IEEE trans. on power systems, Vol. 20, pp. 587-595, May2005, 8. Warsono, et al, Economic Load Dispatch Optimization of Renewable Energy in Power System Using Genetic Algorithm, Paper accepted for the IEEE Powertech Conference 2007 Lausanne, Switzerland, paper no.531, July 2007 9. The Math Work, Genetic Algorithm and Direct Search Toolbox for use with Matlab user's guide, 2 ed: The Math Works inc. 10. Alsumait, J.S. et al, Aplication of pattern search method to power system economic load dispatch, Proc. the 3rd IASTED Asian Conference Power And Energy Systems, Puket, Thailand, p 90-95, April 2007 11. Chen, C.L. and Chen, N. 2001. Direct search method for solving economic dispatch problem considering transmission capacity constraint. IEEE transactions on power systems. Vol. 16, pp. 764-769,Nov. 2001. 12. Wood, A.J. and Wollenberg. 1984. Power generation, operation and control. USA: John Wiley & Sons, Inc. 13. Shapic E. and Balzer, G., Power Fluctuation from a Large Wind Farm, 2005 International Conference on Future Power Systems, Nov. 2005 AUTHOR'S ADDRESS
5. ACKNOWLEDGEMENTS
W. Warsono
The authors would like to thank PT PLN (Indonesian Electricity State Company) for support and facilities as well as Prof. D. A. Bradley for his useful suggestions.
School of Computing and Creative Technologies University of Abertay Dundee Kydd Building, DD1 1HG, Dundee, Scotland, UK Email:
[email protected]
6. REFERENCES 1. EWEA. Wind energy the fact, an analysis of wind energy in the EU-25, 2002. [online]. Available from http://www.ewea.org
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