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Wind power integration studies using a multistage stochastic electricity system model P. Meibom, R. Barth, H. Brand, and C. Weber
Abstract— A large share of integrated wind power causes technical and financial impacts on the operation of the existing electricity system due to the fluctuating behaviour and unpredictability of wind power. The presented stochastic electricity market model optimises the unit commitment considering four kinds of electricity markets (e.g. a spot and balancing market) and taking into account the stochastic behaviour of the wind power generation and of the prediction error. It can be used for the evaluation of varying electricity prices and system costs due to wind power integration and for the investigation of integration measures. Index Terms-- electricity markets, recourse planning, stochastic optimisation, unit commitment, wind power
I. INTRODUCTION
T
HE integration of large amounts of wind power in a liberalised electricity system will impact both the technical operation of the electricity system and the electricity markets. In order to cope with the fluctuations and the partial unpredictability in the wind power production, other units in the power system have to be operated more flexibly to maintain the stability of the power system. Technically this means that larger amounts of wind power will require increased capacities of spinning and non-spinning power reserves and an increased use of these reserves. Moreover, if wind power is concentrated in certain regions, increased wind power generation may lead to bottlenecks in the transmission networks. Economically, these changes in system operation have cost and price implications. Even if wind power production is not bid into the spot market, the feed-in of wind power will affect the spot market prices, since it influences the balance of demand and supply. Moreover they may also impact the functioning and the efficiency of market designs. As substantial amounts of wind power will require increased reserves, the prices on regulating power markets are
This work was carried out within the WILMAR (Wind Power Integration in Liberalised Electricity Markets) project which is supported by the European Community under Contract No. ENK5-CT-2002-00663. R. Barth and H. Brand are with the Institute for Energy Economics and the Rational Use of Energy, University of Stuttgart, Germany (e-mail:
[email protected]) P. Meibom is with Risoe International Laboratory, Roskilde, Denmark (email:
[email protected]) C. Weber is full professor for Energy Management at the University of Duisburg-Essen, Germany (e-mail:
[email protected])
1-4244-1298-6/07/$25.00 ©2007 IEEE.
furthermore expected to change. Yet this is not primarily due to the variability of wind power itself but rather due to the partial unpredictability of wind power. If wind power were varying but perfectly predictable, the conventional power plants would have to be operated also in a more variable way, but this operation could be scheduled on a day-ahead basis and settled on conventional day-ahead spot markets. Hence, it is the unpredictability of wind power which requires an increased use of reserves causing price implications. In general, fundamental unit commitment models can be expected to be a good instrument to estimate such impacts. A general synopsis on unit commitment models gives [1]. To address the effects due to the integration of wind power, recent research focused on deterministic approaches, e.g. [2] [5]. However, deterministic models neglect the uncertainties in predicting the future wind power feed-in. But in an efficient market setting, power plant operators will take into account the prediction uncertainty when deciding on the unit commitment. This will lead to changes in the power plant operation compared to a scheduling based on deterministic expectations, since the unit commitment is usually not separable in time. To consider multiple outcomes of wind power predictions when optimising the unit commitment, the approach of stochastic modelling represents a qualified technique. In fact, stochastic modelling has been used to consider not perfect predictable parameters in the past, compare [6] for an overview. The electricity system model presented includes the uncertainty of wind power forecasts as stochastic parameter. It assumes an efficient market operation by applying stochastic linear programming. With efficient markets, i.e. without market power, market results will correspond to the outcomes of a system-wide optimisation. Thus, cost and price effects due to the integration of wind power derived with this model provide a lower bound to the magnitude of these effects in reality. The generation of the stochastic input to the model is done with the Scenario Tree Tool. A documentation of this tool is found in [7]. II. THE MODEL The fundamental model presented analyses power markets based on an hourly description of generation, transmission and demand, and derives hourly electricity market prices from marginal system operation costs. This is done on the basis of a
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cost minimization of the unit commitment. In this model four electricity markets and one market for heat are included: 1. A day-ahead market for physical delivery of electricity. This market is cleared at 12 o’clock for the following day. The electricity demand is given exogenously. 2. An intra-day market for handling deviations between expected productions agreed upon the day-ahead market and the realized values of production in the actual operation hour. Thus, the demand for regulating power is caused by forecast errors connected to the wind power production. 3. A day-ahead market for automatically activated reserve power (frequency activated or load-flow activated). The demand for these ancillary services is specified exogenously to the model. 4. An intra-day market for positive secondary reserve power mainly to meet the N-1 criterion and to consider the most extreme wind power forecast scenarios. This reserve category can be provided by both spinning and nonspinning units with low start-up times. The demand for positive secondary reserve power is calculated with the Scenario Tree Tool. The demand in a region is determined by aggregating as two stochastically independent parameters the reserve demand necessary to cope with an outage of the largest power plant and the largest wind power forecast error causing up regulation. 5. Due to the interactions of CHP plants with the day-ahead and the intra-day market, an intra-day market for district heating and process heat is also included in model. The heat demand is given exogenously. The model is defined as a stochastic linear programming model [8], [9]. The stochastic part is presented by a scenario tree for possible wind power generation forecasts of the individual hours. The technical consequence of the consideration of the stochastic behaviour of the wind power generation is the partitioning of the decision variables: one part describes the different quantities of power sold or bought at the day-ahead market. Thus they are fixed and do not vary for different scenarios. The other part describes contributions at the intra-day-market both for up and down regulation and depends on the scenarios. Several scenario trees are arranged by rolling planning, see below. With regard to geographical resolution each country in the model is sub-divided into different regions, and the regions are further sub-divided into different areas. Transmission lines connecting regions are modeled as upper limits on the power transmitted between regions with transmission losses proportional to the transmitted power. Thus, regional concentrations of installed wind power capacity, regions with comparable low demand and occurring bottlenecks between the model regions can be considered. The further subdivision into areas allows considering individual district heating grids. Furthermore the model considers: • Operational constraints of conventional power generation units like minimum operation times, minimum down
times, part load efficiencies and start-up times. • Capacity constraints of power and heat generating units as well as electricity and heat storages. • Electricity balances within each region taking power transmission between regions into account. • Heat balances within each area. III. ROLLING PLANNING When analysing a longer time period, it is not possible due to calculation time restrictions to use only one single scenario tree. Thus, multi-stage recursion with rolling planning is applied [10]. In stochastic multi-stage recourse models, there exist two types of decisions: decisions that have to be taken immediately and decisions that can be postponed. The first decisions are called “root decisions” and have to be decided before the uncertain future is known. The latter decisions are called “recourse decisions”. They are taken after some of the uncertain parameters are known and can include actions which might possibly revise the root decisions. Stage 1
Stage 2
Stage 3
Rolling planning period 1
Rolling planning period 2
Rolling planning period 3
Rolling planning period 4
12
15
18
21
00
03
00
Fig. 1. Illustration of the rolling planning and the decision structure in each planning period within half a day.
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Year 2010
Germany Denmark Finland 556.9 39.4 94.2
APPLICATION OF THE MODEL
In the following, exemplary results of an analysis comparing three cases of the installed wind power capacity in the year 2010 are presented. In the 2010_Base case, the forecasted wind power capacities for 2010 are considered for all countries. The 2010_10% case considers for the countries Denmark and Germany the forecasted wind power capacities for 2015 and for the countries Finland, Norway and Sweden wind power capacities equal to cover 10 % of the annual electricity demand. In the 2010_20% case, the wind power capacities for the countries Denmark and Germany are left unchanged according to the 2010_10% case whereas the wind power capacities for the countries Finland, Norway and Sweden are increased to cover 20 % of the annual electricity demand. Table 1 shows the assumed annual electricity demand in the year 2010 and Fig. 4 summarises the resulting wind power capacities in the individual countries. TABLE I Assumed annual electricity demand in 2010 [TWh/a]
Sweden 153.0
2010_Base
35000
2010_10% 30000
2010_20% 25000 20000 15000 10000 5000 0
mk
IV.
Norway 133.3
40000 Wind power capacity [MW]
In the case of a power system with wind power, the power generators have to decide on the amount of electricity bidding into the day-ahead market before the precise wind power production is known (root decision). In most European countries this decision has to be taken at least 12 - 36 hours before the delivery period. And as the wind power prediction is not very accurate, recourse actions are necessary when the delivery hour approaches and the wind power forecast becomes more accurate (recourse decisions). In general, new information about the operational status of the electricity systems arrives on a continuous basis. Hence, an hourly basis for updating information would be most adequate. However, stochastic optimisation models quickly become intractable, since a model with k+1 stages, m stochastic parameters, and n scenarios for each parameter (at each stage) leads to a scenario tree with a total of s = n scenarios. It is therefore necessary to simplify the information arrival and decision structure in the proposed model. Hence, the model steps forward in time using rolling planning with a three hour step holding the individual hours. This decision structure is illustrated in Fig. 1 showing the scenario trees for four planning periods covering half a day. For each planning period a three-stage, stochastic optimisation problem is solved having a deterministic first stage covering three hours, a stochastic second stage with five scenarios covering three hours, and a stochastic third stage with ten scenarios covering a variable number of hours according to the rolling planning period in question. In the planning period 1 the amount of power sold or bought from the day-ahead market is determined. In the subsequent planning periods the variables standing for the amounts of power sold or bought on the dayahead market are fixed to the values found in planning period 1, such that the obligations on the day-ahead market are taking into account when the optimisation of the intra-day market takes place.
Germany
Denmark
Finland
Norway
Sweden
Fig. 4. Wind power capacities of the analysed cases.
The individual power plants are aggregated to unit groups. Thereby the type of the power plant, the used fuel and the efficiency are considered as distinctive feature. This leads to 88 different unit groups for Denmark, 53 for Finland, 77 for Germany, 53 for Norway and 79 for Sweden, respectively. The conventional and hydro power plants show a total installed electrical capacity of 138.9 GW. The assumed fuel prices are summarized in table 2. The CO2 emission allowance price was set to 17 €€2002/MWh. TABLE II Assumed fuel prices Fuel Uranium Natural gas Coal Lignite Fuel oil Light oil
Price [€€ 2002/GJ] 1.7 6.16 2.25 1.05 6.16 7.19
Fuel Orimulsion Peat Muni. Waste Straw Wood Wood (Waste)
Price [€ € 2002/GJ] 1.2 1.5 0 4.4 4.3 4
The analysis has been carried out for the months January and February. During this time period, the share of the wind power production in the total electricity production amounts to 5.8 %, 11.8 % and 15.6 % in the cases 2010_Base, 2010_10% and 2010_20%, respectively. TABLE III COMPARISON OF THE CHANGE IN TOTAL SYSTEM OPERATION COSTS Change in wind power production [TWh ]
Change of operation costs [MEuro]
Value of saved water [MEuro]
Avoided costs per additional wind power production [Euro/MWhWind]
2010_10% / 2010_Base
+10.8
-237.3
+163.3
37.2
2010_20% / 2010_Base
+17.7
-335.2
+294.5
35.5
Case 1 compared with case 2
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The value of the additional wind power production is evaluated by the change of the total system operation costs for the considered time period. This is done by the comparison of the cases 2010_10% and 2010_20% with the case 2010_Base. The results are shown in table 3. With higher wind power penetration, the total operation costs of the system decrease and the value of saved water in hydro storages increases. However, the avoided costs per additional wind power production decreases. This is due to higher specific operation costs of the thermal power plants that operate more often in part-load mode and more frequent start-ups. Further wind power integration studies covering the power systems of Denmark, Finland, Germany, Norway and Sweden have been carried out, e. g. [11]-[13]. V. REFERENCES [1]
[2]
[3] [4] [5]
[6]
[7]
[8] [9] [10]
[11]
[12]
[13]
H.Y. Yamin, “Review on methods of generation scheduling in electric power systems”, Electric Power Systems Research, Vol. 69, numbers 2-3, pp. 227 – 248, 2004 M. Krämer, “Long-term costs of electricity generation in Germany: Optimising the inclusion of wind power”, Wind Engineering, Vol. 28, number 4, pp. 465 – 478, 2004 E. Hirst and J. Hild, “The value of wind energy as a function of wind capacity”, The Electricity Journal, Vol. 17, number 6, pp. 11 – 20, 2004 H. Lund, “Large-scale integration of wind power into different energy systems”, Energy, Vol. 30, number 13, pp. 2402 – 2412, 2005 J.F. DeCarolis and D.W. Keith, “The economics of large-scale wind power in a carbon constrained world”, Energy Policy, Vol. 34, number 4, pp. 395 – 410, 2006 S.W. Wallace, S.-E. Fleten, “Stochastic programming models in energy,” in A. Ruszczynski, A. Shapiro (Eds), Stochastic programming, Handbooks in Operations Research and Management Science 10, Elsevier, North-Holland, pp. 637 – 677, 2003 R. Barth, L. Söder, C. Weber, H. Brand, D. Swider, Deliverable D6.2 (b) – Documentation Methodology of the Scenario Tree Tool, Institute of Energy Economics and the Rational Use of Energy (IER), University of Stuttgart, available from www.wilmar.risoe.dk, 2006 J.R. Birge and F. Louveaux, Introduction to stochastic programming, vol. II., New York, Berlin, Heidelberg: Springer, 2000 P. Kall and S.W. Wallace, Stochastic Programming, Chichester: Wiley, 1994 C.S. Buchanan, K.I.M. McKinnon, G.K. Skondras, “The recourse definition of stochastic linear programming problems within an algebraic modeling language,” Annals of operation research, Vol. 104, numbers 14, pp. 15 – 32, 2001 H. Brand, R. Barth, C. Weber, P. Meibom, D.J. Swider, „Extensions of wind power – effects on markets and costs of integration,” in Proc. 2005 4. Internationale Energiewirtschaftstagung, Vienna P. Meibom, J. Kiviluoma, R. Barth, H. Brand, C. Weber, H. Larsen, „Value of electrical heat boilers and heat pumps for wind power integration,” in Proc. 2006 European Wind Energy Conference, Athen R. Barth, H. Brand, D.J. Swider, C. Weber, P. Meibom, “Regional electricity price differences due to intermittent wind power in Germany – Impact of extended transmission and storage capacities,” International Journal of Global Energy Issues, Vol. 25, numbers 3-4, pp. 276 – 297, 2006
VI. BIOGRAPHIES Rüdiger Barth studied mechanical engineering at the University of Stuttgart, Germany and received his diploma degree in 2003. Since 2003 he works at the Institute of Energy Economics and Rational Use of Energy at the University of Stuttgart, Germany. His research interest is the integration of decentralised generation and of intermittent power sources into liberalised electricity systems.
Heike Brand studied economics and engineering at the University of Karlsruhe, Germany and the University of Groningen, The Netherlands and received the Diploma degree in 1997. Since 1999 she works at the Institute of Energy Economics and Rational Use of Energy at the University of Stuttgart, Germany. Her research interest is in the field of energy optimization models and the incorporation of uncertainties by stochastic programming.
Peter Meibom is Senior Scientist in the System Analysis Department at RISOE National Laboratory. He has a master in physics and mathematics from University of Roskilde and Ph.D. in Energy Planning from the Technical University of Denmark. He was the coordinator of the WILMAR project (ENK5-CT-200200663). The last ten years he has worked with the modeling of energy systems characterized by a large share of renewable energy sources in the system. Christoph Weber holds a Diploma degree in mechanical engineering from the University of Stuttgart, Germany and a Ph.D. in economics from the University of Hohenheim, Germany. Currently he is full professor for energy management at the University of Duisburg-Essen, Germany. His research interest is on the application of mathematical models to describe liberalized energy markets.
