Optimum production plans for thermal power plants in the deregulated electricity market

Energy 31 (2006) 1567–1585 www.elsevier.com/locate/energy

Optimum production plans for thermal power plants in the deregulated electricity market Andrea Lazzaretto, Cristian Carraretto* Department of Mechanical Engineering, University of Padova Via Venezia, 1-35131 Padova, Italy

Abstract The introduction of deregulated markets requires correct operation strategies for the competitiveness of electricity utilities. Optimum strategies are determined in this paper for different groups of thermal power plants using a dynamic programming technique suggested by the authors in a previous paper. Attention focuses here on the ‘Day-Ahead market’ session, considering the viewpoint of a company which manages a power plant or a group of power plants trying to maximize profit over the whole session. To cover different situations that could be met in the market, examples are presented both in case of limits imposed on the total production and when all energies produced are supposed to be accepted by the market. q 2005 Elsevier Ltd. All rights reserved.

1. Introduction The study of the electricity market structure (number and role of the operators, number and characteristics of the sessions, supply and demand mechanism, etc.) is the first action to be undertaken in defining optimum power plants operation strategies [1–3]. Attention focuses here on the ‘Day-Ahead market’ session. In this session, supply offers are submitted for each plant and for each hour of the next day and ranked according to increasing prices, whereas demand bids are ranked in the inverse order. The intersection of the two curves defines the total quantity dispatched and the market clearing price equal to the price of the highest supply offer accepted. All plants dispatched receive the same market clearing price, regardless of the price associated with their offers (Italian market operator—GME [4]). * Corresponding author. Fax: C39 049 827 6785. E-mail address: [email protected] (C. Carraretto). 0360-5442/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2005.05.007

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Nomenclature CC Ci Camo i Ccons i Cfuel i CO&M i Efree

combined cycle power plant total production costs of the ith plant amortization cost (V/h) consumable materials cost (V/h) fuel cost (V/h) operation and maintenance cost (V/h) production over the period of analysis, when no target on the total production is fixed (MW h) Etarget production target to be met over the period of analysis (MW h) N number of power plants p(t) hour electricity price forecast at time t (V/MW h) Pi(t) load level of the ith power plant at time t (MW) Pmax,i maximum load level of the ith power plant (MW) Pmin,i minimum load level of the ith power plant (MW) ST steam power plant DPdown,i(t) maximum power decrease in Dtt (MW) DPup,i(t) maximum power increase in Dtt (MW) DT total period of analysis (h) Dtmin,off minimum periods for shut-down (h) Dtmin,on Minimum periods for start-up (h) Single time interval (from the generic time index tK1 to the time index t) (h) Dtt Pi(DT) total profit of the ith power plant over the period of analysis DT (V) pi(Dtt) profit of the ith power plant during the generic time interval Dtt (V) t time index (tZ1,2,.,T) time index at which the plant switch-off begins toff time index at which the plant start-up begins ton We consider here the viewpoint of a company which manages a plant or a group of plants in the market, trying to get the maximum profit. We work under the hypothesis that the company has no capability of modifying market clearing price by means of its supply offers, in the sense that it does not conduct speculative strategies, for instance, by offering electricity at prices much lower than real costs to increase market share. Collusive strategies between producers [5–6], still for speculative purposes, are also not considered. In this context, it is reasonable to search for optimum plant management strategies under hourly price forecasts deriving from market analyses based on the equilibrium between existing producers. We do not refer to a specific producer, but we analyze several thermal power plants of different type and size and some possible combinations of these plants. The first step of the work consists in identifying conditions (electricity price and fuel cost combinations) in which each plant separately can operate conveniently in the market. This is done by evaluating the range of loads of convenient operation in which a positive profit can be obtained under fixed production costs.

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Then, an optimum operation strategy over the period of interest is found for the single plant or the group of plants belonging to the company. The optimization approach is that proposed in a previous paper [7], in which the authors suggested a dynamic programming technique to determine this strategy under all technical constraints during plant operation and fixed price forecasts. Plant characteristic curves are to be known and can be obtained directly from experimental data or by a numerical simulator taking into account design and off-design performance correctly. The paper focuses on typical thermal power plants: – steam power plants (oil or coal fuelled); – combined cycles power plants (two or three pressure levels with or without reheat). To cover different situations that could be met in the market, examples of optimum strategies are shown both in case of limits imposed on the total production over the period of interest (e.g. by existing contracts with customers) and when all the energies produced are supposed to be accepted by the market.

2. Power plants modeling Profit deriving by plant operation can be determined by correctly evaluating the fuel consumption vs. electric power curve. In fact, fuel represents the main cost term among production costs, and power generates incomes depending on electricity prices. A large set of historical data or a simulator is required to obtain this curve. In most cases, a detailed model of each plant component is not necessary and the plant can be considered as a single black-box when reliable data on power and fuel consumption are available. In any case, a precise performance evaluation of plant operation requires a continuous update using a data acquisition system. However, very often only some quantities are measured or the accuracy of measured data is not too high, and a whole data set is available just for performance tests. Moreover, component deterioration or maintenance interventions may modify operating conditions. Numerical simulators are useful when measured data are not sufficient to evaluate plant performance. Result accuracy is in any case improved by tuning the models with actual data. ‘Adaptive’ models can be used to determine plant behavior under actual conditions. Detailed models at component level can be useful to predict effects of component deterioration, variable set points of control system, maintenance actions or design modifications on total plant performance. Here a modular code is used—the DIMAP code, developed at the Department of Mechanical Engineering of the University of Padova [8] which helps to build various plant configurations and analyze effects of different design choices. The model evaluates steady state performance at design and off-design conditions. To improve accuracy, single-component thermodynamic quantities are adjusted on real operation data depending on the specific plant analyzed. Control system actions are taken into account by including the correct laws (derived from experimental data) for controlled parameters. Steam and combined cycle power plants of different sizes are analyzed in this work: – 320 and 165 MW coal- or oil-fired steam (ST) power plants; – 380 and 100 MW natural gas combined cycle (CC) power plants having three and two pressure levels with and without reheat, respectively.

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The main characteristics at design conditions of these plants are shown in Tables 1 and 2. Efficiency vs. load level curves, calculated using the DIMAP code, are represented in Fig. 1.

3. Ranges of convenient operation for different thermal power plants As first action, to identify conditions in which the plant can operate conveniently in the market, plant performance and profit for possible ranges of variation of fuel costs and electricity prices are evaluated [7]. This is done separately for each plant to be managed by a company. Production costs (Ci) of the ith power plant, when operated at the generic load level Pi during a given period of time Dtt, are assumed to be the sum of the following terms

 Ci Pi Dtt Z Cifuel C CiO&M C Cicons C Ciamo (1) O&M , Ccons and Camo are the costs associated with fuel consumption, operation and where Cfuel i , Ci i i maintenance, consumable materials and amortization, respectively. Cost data (Table 3) used in the analyses were taken from several sources:

– from US Department of Energy [9] for the 320 MW coal-fired ST power plant and the 380 MW CC plant; – from ENEL, the main Italian electricity utility, for the 165 (oil and coal) and 320 MW (oil) ST power plants. The costs of the 100 MW CC plant were derived from the 380 MW one by using the ratio between power (380/100)0.6 on the basis of available data for plants of similar size as scaling factor. The range of convenient operation is defined in the load-price diagram by calculating the area associated with profits (pi) assuming non-negative values (Fig. 2). The left and right bounds of this area are the minimum and maximum technical load levels, whereas the bottom limit corresponds to the ‘zeroprofit’ curve. For a fixed load level, a corresponding point on this curve is determined by calculating the electricity price giving a zero-profit: Table 1 Design characteristics of the steam power plants running on coal and oil Coal plants Gross power (MW) Electric efficiency (%) Feed-water mass flow rate (kg/s) Superheated steam Pressure (bar) Temperature (8C) Reheated steam Pressure (bar) Temperature (8C) Condenser pressure (bar)

Oil plants

165 36.4 144.4

320 38.1 293.3

165 37.2 141.4

320 40.7 293.3

141 536

178 538

141 536

178 538

34 536 0.050

33 538

38 536 0.050

33 538

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Table 2 Design characteristics of the combined cycle power plants

Gross power (MW) Electric efficiency (%) Gas turbine Power (MW) Inlet air mass flow (kg/s) Pressure ratio Turbine inlet temperature (8C) Turbine outlet temperature (8C) High pressure steam Mass flow rate (kg/s) Pressure (bar) Temperature (8C) Intermediate pressure steam Mass flow rate (kg/s) Pressure (bar) Temperature Low pressure steam Mass flow rate (kg/s) Pressure (bar) Temperature (8C) Condenser pressure (bar)




pi Dtt



100 MW CC plant (two pressure levels)

380 MW CC plant (three pressure levelsCreheat)

100 52.4 Siemens V64.3 61.5 183.3 15.6 1120 534

380 MW 55.1 GE MS9001FA 265 624 15.5 1288 610

21 80 535

78.9 100 565

– – –

10.8 23 565

7 4 240 0.055

12.4 2.2 280 0.040




 Ci Pi Dtt
 Z 0/ p Dtt jpi ðDtt ÞZ0 Z Pi Dti

(2)

By repeating this calculation for each feasible load level, the zero-profit curve can be drawn, as shown for example in Fig. 2, for a 320 MW coal-fired steam power plant. For the chosen cost scenario (only variable cost terms), a positive profit can be obtained for electricity prices higher than 25 V/MW h at 55%

380MW CC Plant 100MW CC Plant

Efficiency

50% 45% 320MW Steam Plant (Coal)

320MW Steam Plant (Oil)

40% 35% 30% 30%

165MW Steam Plant(Coal) 165MW Steam Plant (Oil) 40%

50% 60% 70% 80% Load Level [% of Pmax ]

90%

100%

Fig. 1. Efficiency vs. load level curves for different power plants (ISO conditions).

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Table 3 Fixed and variable cost terms for different ST and CC power plants

165 MW (oil) 165 MW (coal) 320 MW (oil) 320 MW (coal) 100 MW 380 MW

Capital cost (V/kW-yr)

Fixed O&M cost (V/kW–yr)

Variable O&M cost (V/MW h)

Consumable operating cost (V/MW h)

ST plant

92.8

30.1

0.89

3.27

ST plant

98.6

37.7

0.74

4.76

ST plant

66.7

18.2

0.56

2.80

ST plant

70.8

25.3

0.50

3.20

CC plant CC plant

61.7 27.5

20.3 11.5

1.76 1.00

0.86 0.50

The fuel cost depends on the actual load level of the plant, its efficiency at the actual load level (see Fig. 1 for example), and the unit cost of the fuel (coal 56.8 V/t; oil 175.6 V/t; natural gas 222.1 V/t).

maximum efficiency operation (around 300 MW). At different load levels, this minimum electricity price increases because of the reduced plant efficiency. The area of positive profit can be evaluated under two hypotheses: (a) by including only the variable cost terms in Eq. (1); (b) by including variable and fixed cost terms in Eq. (1). Case (a) generally applies when searching for the convenient operation conditions of an existing plant, case (b) being more suitable when studying different design options. Examples of the two cases are shown in the following. 3.1. Variable costs

Electricity Price [= /MWh]

The area of positive profit calculated on the basis of the only variable costs helps to determine the operation flexibility of existing power plants under variations of production costs and energy prices. So, for different existing plants, it makes possible to compare the ranges of convenient operation at constant electricity price or, conversely, the minimum acceptable electricity prices at constant load level. 40 38 36 34 32 30 28 26 24 22 20

Area of convenient operation

Zero profit curve 0

50

100

150 200 Load Level [MW]

250

300

350

Fig. 2. Example of an area of convenient production for a 320 MW coal-fired ST power plant.

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Fig. 3 presents the zero-profit curves of the considered power plants for different values of the variable cost terms associated with fuel and O&M. From this figure we observe: (i) For all plants, the different relative weight of variations of the fuel and O&M terms on total variable costs is immediately apparent. It is also clear how changes in these cost terms directly affect the zero-profit curve, and, in particular, the minimum acceptable energy price. 320MW Coal Fired Steam Plant

60

(b)

Actual costs Fuel costs –20% Fuel costs +20% Fuel and O&M costs –20% Fuel and O&M costs +20%

55 50 45

Electricity Price [= /MWh]

Electricity Price [= /MWh]

(a)

40 35 30

20%

30%

(c)

40%

50% 60% 70% Load Level [%]

80%

90% 100%

45 40 35

Actual costs Fuel costs –20% Fuel costs +20% Fuel and O&M costs –20% Fuel and O&M costs +20%

30

20%

30%

(d)

165MW Coal Fired Steam Plant

40%

50% 60% 70% Load Level [%]

80%

90% 100%

165MW Oil Fired Steam Plant 60

60 Actual costs Fuel costs –20% Fuel costs +20% Fuel and O&M costs –20% Fuel and O&M costs +20%

55 50 45

Electricity Price [= /MWh]

Electricity Price [= /MWh]

50

20

20

40 35 30

55 50 45 40 35 30 25

25

20 20%

20 30%

40%

(e)

50% 60% 70% Load Level [%]

80%

90% 100%

100MW CC Plant 60 55 50 45

Actual costs Fuel costs –20% Fuel costs +20% Fuel and O&M costs –20% Fuel and O&M costs +20% 30%

40%

(f)

Actual costs Fuel costs –20% Fuel costs +20% Fuel and O&M costs –20% Fuel and O&M costs +20%

40 35 30 25

50% 60% 70% Load Level [%]

80%

90% 100%

380MW CCPlant 60

Electricity Price [= /MWh]

20%

Electricity Price [= /MWh]

55

25

25

20

320MW Oil FiredSteamPlant

60

Actual costs Fuel costs –20% Fuel costs +20% Fuel and O&M costs –20% Fuel and O&M costs +20%

55 50 45 40 35 30 25

20%

30%

40%

50% 60% 70% Load Level [%]

80%

90% 100%

20 20%

30%

40%

50% 60% 70% Load Level [%]

80%

90% 100%

Fig. 3. Effect of fuel and O&M costs on the lower bound of the area of convenient production for different steam and combined cycle power plants (variable costs only).

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(ii) Due to the higher value of the unit cost of fuel (coal 56.8 V/t, oil 175.6 V/t), the 320 MW oilfired ST power plant shows a worse behavior at part load conditions than the corresponding coalfired one in terms of profit (higher slope of the curve), despite of the similar efficiency curves of the two plants (Fig. 3a and b). This implies bigger variations of the area of convenient operation for the same relative change in the fuel unit cost (C20% and K20% in the figures) as well. (iii) A smaller plant size (165 vs. 320 MW) at the same unit cost of fuel implies a reduction of the convenient area as clearly appears by comparing Fig 3a and c, or Fig. 3b and d, for coal and oil, respectively. (iv) The zero-profit curves of the CC power plants lay between those of the ST plants of equivalent size running on oil and coal, being closer to the latter at high load levels and to the former at low load levels, because of the different part-load behavior (compare Fig. 3a, b and f). Thus, when the only variable cost terms in Eq. (1) are considered, CC plants demonstrate to be less convenient than coalfired ST plants and more sensitive to energy price variations. Size effects are similar to those already observed for the ST plants (see Fig. 3e and f) and are dependent on the mentioned cost assumptions.

3.2. Variable and fixed costs When both the variable and the fixed costs are used to determine the zero-profit curve of a given power plant, the numerator of the Eq. (2) changes. As a result, the associated zero-profit curve is modified both in absolute values and in slope over the entire load range. Introducing the fixed costs in the analysis may be of help in comparing different design options. This happens, for instance, in planning the expansion of the production capacity. In this case, to find the zeroprofit curve in the electricity price–load diagram, a proper load factor is to be assumed to convert the annual fixed costs (V/kW yr) into costs per unit of electric energy produced (V/MW h). Parametric analyses under variations of this factor can then be performed. An example is shown in Fig. 4 for the 320 MW ST power plants (coal- and oil-fired) and the 380 MW CC power plant, using a 0.8 load factor. Under these assumptions, since the total fixed costs of the combined cycle unit are about half those of the steam plants (see Table 3), the CC plant becomes more 75 Electricity Price [= /MWh]

70 320MW Oil Fired Steam Plant

65 60 55 50

320MW Coal Fired Steam Plant

45 40

380MW CC Plant

35 30 30%

40%

50%

60% 70% Load Level [%]

80%

90%

100%

Fig. 4. Comparison of the lower bound of the areas of convenient production of different power plants considering variable and fixed cost terms.

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advantageous than the coal ST one over the whole operating range, the zero-profit curves being, however, very close around full load conditions. A comparison between a generic zero-profit curve and possible trends for hourly electricity prices is shown in Fig. 5.

4. Optimum management strategies in the day-ahead market A dynamic approach is proposed in [7] to find the optimum production plan of a power plant or a group of power plants, consisting of the sequence of load levels of each unit that maximizes the total profit in the period of interest (DT). This period is uniformly divided into T time intervals. Time intervals, typically 1-h long, are labeled using the time index t (tZ0,.,T): the generic time interval Dtt ranges from the time index tK1 to the time index t. In each interval, electricity market clearing price p(Dtt) and unit production costs (Table 3) are supposed to be known from available forecasts. The total profit P to be maximized over DT is max PðDT Þ Z Pi

T X N 
X 


 p Dtt Pi Dtt K Ci Pi Dtt Dtt

(3)

tZ1 iZ1

where N is the number of plants, Pi(Dtt) is the load level of the ith plant in the time interval Dtt and Ci are the production costs associated with Pi(Dtt). Constraints on minimum and maximum feasible plant load levels (a), ramp rates (b), minimum start up (c) and shut-down (d) periods are considered: (a)

pi,min P(pi,min) Load level

Load level Electricity price

Electricity price

(



 Pmin;i Dtt % Pi Dtt % Pmax;i Dtt Pi Dtt 0

(4)

Pmax Pmin Time

Time

Time

Fig. 5. Load adjustment according to electricity price trends and plant ‘zero-profit’ curve.

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(b)

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 Load increase : Pi Dtt K Pi DttK1 % DPup;i Dtt

(5)




 Load decrease : Pi DttK1 K Pi Dtt % DPdown;i Dtt

(6)

(c) If

t X

Dt4 % Dtmin;on ;


 Pi Dtt Z 0

(7)

Dt4 O Dtmin;on ;



 Pi Dtt R Pmin;i Dtt

(8)

Dt4 % Dtmin;off ;



 Pi Dtt R Pmin;i Dtt

(9)

Dt4 O Dtmin;off ;


 Pi Dtt Z 0

4Zton

If

t X 4Zton

(d) If

t X 4Ztoff

If

t X

(10)

4Ztoff

where: – DPup,i(Dtt) and DPdown,i(Dtt) are the maximum power increase and decrease in Dtt; – ton is the time index at which start-up begins, and Dtmin,on is the minimum period for start-up; – toff is the time index at which switch-off begins, and Dtmin,off is the minimum period for shutdown. According to the number of times in which plant is shutdown or plant load is modified, further costs should be added to the production costs to account for additional maintenance interventions and/or shortening of component operation life. These costs might be quite important, e.g. in big steam power plants. However, the difficulty in their estimation may lead to uncertain comparisons among different solutions. Thus, they are not considered in this work. Two different production schedules can be defined depending on the limits that may exist on the total electricity production of the group of power plants [7]: (1) No limits on the total production (Free electricity production). If there is no target or limit on the total production in the overall period of interest DT, the load level of each plant belonging to the group has no influence on the load levels of the others. Thus, each power plant production schedule can be determined separately, and the optimal overall production of the group is the sum of the production of all plants. 2) Total electricity production limited (Fixed electricity production). The total electricity production of the group of power plants over the period of interest is fixed (Etarget)

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according to the company policy or because of existing limits in the market: T X N X


 Pi Dtt Dtt Z Etarget

(11)

tZ0 iZ1

In case of free production, the dynamic approach considers all the feasible load levels in each time interval deriving from constraints (a)–(d) and finds loads that maximize the total profit P (Eq. (3)). Electricity Price [= /MWh]

(a) 110 100 90 80 70 60 50 40 30 20 10

0

3

Load level [MW]

(b) 180 160 140 120 100 80 60 40 20 0

6

9

12

15

18

21

24

165MW Oil ST Plant 165MW Coal STPlant

0

3

6

9

12

15

18

21

24

(c) 350

Load level [MW]

300 250 200 320MW Oil ST Plant

320MW Coal ST Plant

150 100 50 0

0

3

6

(d) 450 400 350 300 250 200 150 100 50

12

15

18

21

24

18

21

24

380MW CC Plant

Load level [MW]

0

9

100MW CC Plant

0

3

6

9

12

15

Fig. 6. Optimum free electricity production plans for a typical winter day.

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In case of fixed production, the procedure finds the profit-maximizing combinations of loads in order to apportion Etarget among the time intervals. Various targets in the total electricity production can be analyzed to comply with forecasted market restrictions or market share increases (according to planned levels of the electricity production quota).

Electricity Price [= /MWh]

(a) 110 100 90 80 70 60 50 40 30 20 10 0

3

6

9

Load level [MW]

(b) 180 165MW Coal ST 160 Plant 140 120 100 80 60 40 20 0 0 3 6

12

15

18

21

24

21

24

165MW Oil STPlant

9

12

15

18

(c) 350 Load level [MW]

300 250 200 320MW Oil ST Plant

150 100

320MW Coal STPlant

50 0 0

3

6

9

12

15

18

21

24

15

18

21

24

(d) 400 Load level [MW]

350 380MW CC Plant

300 250 200 150

100MW CC Plant

100 50 0

0

3

6

9

12

Fig. 7. Optimum free electricity production plans for a typical summer day.

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5. Examples of application The following cases of optimized strategies are presented under various hourly electricity price trends related to different seasons: (1) free production for a group of different (in size, number and type) power plants; (2a)fixed production (one or more targets) for the group of point 1; (2b)fixed production (one or more targets) for different groups of power plants. In case (1), as mentioned in Section 4, the total production of the whole group in DT is the sum of the productions (determined separately) of all plants. This is the ‘reference’ optimum production (Efree) for given market conditions and plant performance characteristics. Different production targets are imposed in case (2a), both higher or lower than the ‘reference’ one, to investigate the capability of the group of plants of reacting to demand restrictions or expansions. Case (2b) is then used to compare the different optimum strategies of various groups of plants (characterized by different type, number and size) in the same market conditions. This case is considered to foresee possible changes in the compositions of the group because of old plant shut-off or entries of new higher efficiency plants. 5.1. Case 1: Free electricity production Optimum strategies are determined for two electricity price trend forecasts of typical winter (Fig. 6a) and summer (Fig. 7a) days. By comparing the daily price trend with the minimum value of the electricity price pi,min (Fig. 5) in the zero-profit curve associated with a specific plant, it appears immediately if the plant can operate profitably at least in one time interval of the whole period DT. If pi,min is lower than the minimum value of the market clearing price forecasted, plant operation is always convenient. Conversely, if pi,min is always higher than the maximum clearing price, plant operation is never convenient. Load variations, being determined by the optimization procedure, are expected in intermediate situations. The electricity price curve in Fig. 6a (winter day) is always above pi,min for both the 165 and 320 MW coal ST power plants and for the CC plants, whereas it intersects the zero-profit curve of the oil ST plants (compare Fig. 6a with Fig. 3); accordingly, load is not constant for the latter (see Fig 6b–d). Conversely, in a typical summer day all plants operate under variable load since the price curve (Fig. 7a) intersects the zero-profit curve for each of them. Coal ST and CC plants work at full load during daytime (from 6 a.m. to 8 p.m.) and at minimum load during the night. Instead, the optimum strategy of the oil ST plants Table 4 Groups of power plants analyzed

Group 1 (70% ST–30% CC) Group 2 (50% ST–50% CC) Group 3 (30% ST–70% CC)

Coal

Oil

Gas

2!165 MW 3!320 MW 4!165 MW 1!320 MW 0!165 MW 1!320 MW

3!165 MW 2!320 MW 4!165 MW 1!320 MW 1!165 MW 1!320 MW

3!100 MW 1!380 MW 1!100 MW 4!380 MW 4!100 MW 5!380 MW

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indicates partial load operation during daytime as well, depending on the higher zero-profit curve and lower ramp rate values. Note that the area below the curve in the load–time diagrams represents the plant production in the whole period. Thus, the total production of the group is determined by summing the areas associated with all plants. This is the ‘reference’ optimum production target Efree. The ratio between Efree and the maximum possible production at design conditions corresponds to the ‘reference’ average daily load factor, and gives the percentage of the production capacity exploited in the market scenario considered. As an example, for the Group 1 in Table 4, this load factor is equal to 95% in the winter day of Fig. 6, and to 75% in the summer day of Fig. 7.

Elec. Price [ /MWh]

(a) 70 60 50 40 30 20 10 0 (b)

3

6

9

12

15

18

21

24

18

21

24

320MW Coal Fired Steam Plant

Load level [MW]

320 270 220 67GWh 65GWh (Free production) 50GWh 40GWh

170 120

0

(c)

3

6

9

12

15

320MW Oil Fired Steam Plant

Load level [MW]

320 65GWh (Free production) 270 50GWh 220 170 40GWh

120 0 (d)

3

6

9

12

15

18

21

24

380MW Combined Cycle Plant

380

Load level [MW]

67GWh

330 280 230 67GWh 65GWh (Free production) 40GWh 50GWh

180 130 80 0

3

6

9

12

15

18

21

24

Fig. 8. Optimum electricity production plans of the Group 1 for various total production targets during a typical autumn day.

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5.2. Case 2: Fixed electricity production Optimization strategies are evaluated in the following for various groups of power plants and different values of Etarget in the period of interest. In particular, as listed in Table 4, three groups have been examined: – Group 1, approximately corresponding to the actual situation of thermal power plants in the Italian electricity system (about 70% of the capacity deriving from ST plants and 30% from CC plants); – Group 2, including 50% of ST plants and 50% of CC plants; Elec. Price [ /MWh]

(a) 70 60 50 40 30 20 10 0 (b)

3

6

9

12

15

18

21

24

18

21

24

18

21

24

18

21

24

320MW Coal Fired Steam Plant

Load level [MW]

320 270 220 67GWh (Free production) 65GWh 50GWh 40GWh

170 120 0

(c)

3

6

9

12

15

320MW Oil Fired Steam Plant

Load level [MW]

320 67GWh (Free production) 65GWh 50GWh 40GWh: plant shut-down

270 220 170 120 0

(d)

6

9

12

15

380MW Combined Cycle Plant

380

Load level [MW]

3

330 280 230 67GWh (Free production) 180

65GWh

130

50GWh 40GWh

80

0

3

6

9

12

15

Fig. 9. Optimum electricity production plans of the Group 3 for various total production targets during a typical autumn day.

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– Group 3, corresponding to a hypothetical configuration in which about 70% of the power capacity is supplied by CC plants and the rest almost entirely covered by coal ST plants.

(a)

3000

Total load level [MW]

The optimization procedure was first applied to the three groups using a typical autumn day electricity price curve shown in Fig. 8a. Results are presented in Figs. 8 and 9 for some of the plants belonging to Groups 1 and 3, respectively. The thick lines in these figures represent the ‘reference’ optimum group production Efree, determined by optimizing each plant production separately. Efree is equal to 65 and 67 GW h for Groups 1 and 3, respectively, corresponding to average daily load factors of about 87% and 90%. The other curves are associated with different values of Etarget, higher or lower than Efree. It is apparent that the value of Etarget affects in a different way the optimum strategies of the single plants, either belonging to Groups 1 or 3. When Etarget is decreased, the production tends to concentrate in peak hours. Conversely, an increase in Etarget enlarges the full-load operation periods for all plants. The priority in plant operation depends on production costs: the lower the variable production costs the higher the priority. Accordingly, coal ST plants operate with the highest priority, followed by CC and oil ST plants. Consequently, coal ST plants tend to work with high load factor (close to that of the free production condition); CC plants operate with little lower load factors (and concentrating the production in peak hours also because of the faster load ramps-compare Fig. 8b and d); oil ST plants work only ‘if necessary’. A further consequence of plant operation priority is that less advantageous plants (oil ST) show lower average load factor at the same value of Etarget when the percentage of plants operating at lower production costs (coal ST and CC plants) is higher (Group 3). So, the 320 MW oil ST plants are shut down all day long when Etarget is lower than 50 or 35 GW h if they belong to Group 3 or 1, respectively (Figs. 8c and 9c). This also appears from Fig. 10a and b showing the total production of the whole groups

2500

Group #1. 40GWh

CC Oil ST Coal ST

2000 1500 1000 500 0 0

Total load level [MW]

(b) 3000 2500

1

2

3

4

5

6

Group #3. 40GWh

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

CC Oil ST Coal ST

2000 1500 1000 500 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Fig. 10. Comparison of the hourly total production for Groups 1 and 3, respectively, for a production target of 40 GW h in a typical autumn day.

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and the fraction covered by each plant type for EtargetZ40 GW h. Comparing the two figures it appears that in Group 3: (i) oil ST plants are shut down since their contribution is no longer necessary; (ii) CC plants cover a bigger fraction of Etarget because of the higher fraction of installed power; (iii) coal ST plants work with high load factors, similar to those of Group 1, because of their highest operation priority. a) Winter day

Total daily profit [%]

100%

Group #1 Group #2 Group #3

90%

80% 50

55

60

65

70

75

Total daily electricity production (E target) [GWh] b) Summer day

Total daily profit [%]

15%

100MW CC Plant Shut-down

Group #1 Group #2 Group #3

320MW Oil ST Plant Shut-down

10%

5% 165MW Oil ST Plant Shut-down

0% 15

20

25

30

35

40

45

50

55

60

65

70

75

– 5%

Total daily electricity production (E target) [GWh] c) Autumn day 320MW Oil ST Plant Shut-down

Total daily profit [%]

30% 25% 20%

165MW Oil ST Plant Shut-down

15% Group #1 Group #2 Group #3

10% 5% 100MW CC Plant Shut-down 0%

15

20

25

30

35

40

45

50

55

60

65

70

75

Total daily electricity production (E target) [GWh]

Fig. 11. Total profit (with variable costs only) vs. production target over different seasons typical days (reference: winter day maximum profit of Group 3).

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The daily total profits obtained by each of the three groups versus the daily total production are shown in Fig. 11 for different typical days of the year. Calculations are still performed using only variable production costs to compare the three groups in terms of short period planning. Fig. 11a–c refers to winter, summer and autumn days, respectively. In general, groups including a higher percentage of high operation priority plants (coal ST and CC) are more profitable independent of the total production level. Consequently, when the shut-down of low priority plants is not convenient or not possible, either because of high electricity prices or high production targets, Group 3 performs better, whereas Group 1 generates the lowest profits because of the highest oil ST power fraction. When, conversely, plant shutdown is convenient or possible because of the low production level and/or low electricity prices, Group 1 becomes the best solution because, among plants still in operation, the percentage of those performing better at part load levels is higher than in Group 3. A clearer scenario appears on an annual basis, when fixed production costs in Eq. (1) are included in the analysis (Fig. 12). Group 3 generates the maximum profits regardless of the total production level mainly due to the low fixed costs of the CC plants.

6. Conclusions The several analyses conducted in this paper demonstrated the effectiveness of a dynamic approach to determine optimal strategies for single power plants or groups of power plants under various electricity price and fuel cost forecasts. Examples were given for groups of thermal power plants having different composition. For each plant belonging to a group, the production schedule and the different capability to operate conveniently within the entire group were determined, depending on the composition of the group and the strategic objectives on the total group production. A preliminary analysis to find the load ranges of convenient operation of single plants (according to market values of electricity prices and fuel costs) has shown to be very helpful in interpreting results of the optimization procedure, especially when several units having different operating and economic characteristics are considered. Optimizations were performed using variable production costs to evaluate short-term strategies alone, or including the fixed terms for power expansion/reduction planning as well. Although strategies do not differ in the two cases in a given market scenario, the evaluation of the total profits in the period of 100%

Total profit [%]

80% 60%

40% Group #1 20%

Group #2 Group #3

0% 10000

12500

15000

17500

20000

22500

25000

27500

Total production level (E target) [GWh]

Fig. 12. Total annual profit (with variable and fixed costs) vs. production target (reference: maximum profit of Group 3).

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interest helps to identify conditions under which total fixed cost recovery is not possible, i.e. when the firm cannot operate profitably unless modifications in the market equilibrium occur.

References [1] Newbery, D. Competition, contracts and entry in the electricity market. Proceedings of the royal economic society conference; 1996. [2] Wolak FA, Patrick RH. The impact of market rules and market structure on the price determination process in the England and Wales electricity market. POWER paper PWP-047. Berkeley, CA: University of California Energy Institute; 1996. [3] Hogan WW. A market power model with strategic interaction in electricity networks. Energy J 1997;18(4). [4] GME. Electricity market rules. Italian Legislative Decree 79/99 of March 16th; 1999 [5] Borenstein S, Bushnell J, Knittel CR. Market power in electricity markets: beyond concentration measures. POWER working paper PWP-059r. Berkeley, CA: University of California Energy Institute; 1999. [6] Rudkevich A, Duckworth M, Rosen RA. Modeling electricity pricing in a deregulated generation industry: the potential for oligopoly pricing in a Poolco. Energy J 1998;19(3). [7] Carraretto C, Lazzaretto A. On the electrical energy dispatch in the Italian deregulated market. In: ECOS 2002, on efficiency, cost, optimization, simulation and environmental aspects of energy systems, Berlin, Germany, vol. I; 2002. p. 400–8. [8] Lazzaretto A, Macor A, Mirandola A, Stoppato A, Donatini F. DIMAP, a modular computer code for the thermodynamic, exergetic and thermoeconomic simulation of energy systems. In: Winter annual meeting of the ASME, vol. 35. San Francisco, CA: AES. ASME; 1995. p. 119–26. [9] US DOE. Office for fossil energy. Market-based advanced coal power systems, final report. Washington, DC: US DOE; 2000.