Simulation of pump storage plants

Pump Storage plants can be used to balance the electricity system. In times of low electricity prices electricity is used to pump water to a storage on higher ground. In cases of peak prices

the water is used to generate electricity. Currently pump storage plants represent the most important way to store electricity in an indirect way. In order to integrate pump storage plants into the simulation of electricity markets two procedures have been developed. The first pro-cedure relies on a static profile, the second propro-cedure simulates pump storage plants in a dy-namic way.

5.5.1 Static simulation

In the static simulation the utilization of pump storage power plants is integrated as an exoge-nous load curve which is based on the available information. An overview of the pump stor-age profile applied for every simulation day is given in Figure 5-15. In order to force the pump storage profile into the market, a price independent bid is placed on the spot market. If this setting is applied, pump storage plants cannot bid into the reserve markets. The advantage of this solution is that in this setting pump storage plants do not interact with other effects in the market. This can be useful for the analysis of single effects. Another aspect is that it helps to save computational resources.

-3,000 -2,500 -2,000 -1,500 -1,000 -500 0 500 1,000 1,500 2,000 2,500

1 3 5 7 9 11 13 15 17 19 21 23

Hour

Load in MW

Generation mode

Pump mode

Figure 5-15: Pump storage load profile

Source: Verband der Elektrizitätswirtschaft [VDEW], 2000

5.5.2 Dynamic simulation

The dynamic simulation of pump storage power plants is a complex issue since pump storage can bid on several markets. Another important issue is the fact that technical restrictions such as the storage volume have to be taken into account. The basic input for the dynamic simula-tion is a database on the German pump storage plants. It is given in the Appendix. The core of the simulation of pump storage plants is to determine an optimal utilization of the plants based on given technical restrictions. The first step is creating a price prognosis for a given period. The price prognosis is created according to the algorithm described in 5.3.6. In order to determine the maximum income and the corresponding utilization of a given plant an

algo-rithm is developed which optimizes the utilization of each pump storage plant. The mathe-matical formulation of the algorithm is given in Formula 5-11. If the trading on the minute reserve market for pump storage plants needs to be integrated into the simulation, the algo-rithm can be extended according to the next formula.

Formula 5-11: Algorithm for the utilization of pump storage power plants

∑

Formula 5-12: Optimization of pump storage plants on spot market and reserve market

⎩⎨

The actual calculation within the simulation platform is carried out by sorting the price fore-cast in ascending and descending order. In the next step the algorithm cycles through both price lists and matches price pairs of both lists as long the operation of generation in hour x and pumping in hour y creates a positive income with the given efficiency of the plant. After matching a pair of prices, the maximum capacity for operation in both hours is determined by checking the storage status and the capacity of the plant for the entire period. Another

condi-tion for the algorithm is that the initial storage status is equal to the storage status at the end of the planning period. For the analysis carried out in this thesis it is assumed that the initial storage status is 50 % of the total storage volume. Based on this algorithm the optimal utiliza-tion of each pump storage plant can be calculated for any period.

Another problem which has to be taken into account is that the operation of a pump storage plant with a capacity of several hundred MW can have an impact on the prices itself. There-fore the algorithm can also be used with an option which creates a new price There-forecast for every plant by considering the planned operation for the previous plant.

After the development of an algorithm for the optimal utilization of every pump storage plant the next issue is to determine the bidding behaviour on the electricity markets. Since primary reserve is activated automatically within running generation units it is assumed that pump storage plants do not bid into the primary reserve market due to technical restrictions. The secondary reserve market is an interesting market for pump storage plants as they can meet the technical requirements. In addition capacity payments in this market are relatively high.

The next market is the minute reserve market. Since the actual utilization of the minute re-serve is rather low, the balancing capabilities of pump storage plants are wasted in the market.

Therefore it is assumed in the case studies of this thesis that pump storage plants to do not bid into the minute reserve market, which also helps to simplify the problem. The remaining spot market is a very attractive market for pump storage plants since they can create profits on volatile market prices. As consequence of the discussion above pump storage plants can bid into the secondary reserve market and the spot market for the simulations within this thesis.

As described in 5.4.2.2, the secondary reserve market is executed once per year within the model. In order to determine the capacity price for the bid into the secondary reserve market the possible profits of the alternative operations on the spot market for the analysed period have to be calculated. Although the algorithm is capable to do that, the calculation time of the algorithm for the optimization of 32 plants for a time horizon of 8760 hours is unbearable for a simulation model as the time needed for the calculation grows in a non-linear way. The time horizon for the calculation of the potential average daily income for pump storage plants on the spot market can be varied. In order to determine the impact of the time horizon on the cal-culation time, the time horizon is varied and the required time for one simulation run of one year is determined. The results of this procedure are presented in Figure 5-16. The experiment is carried out on a fast desktop PC⁷. The results show that the influence of the pump storage algorithm on calculation times is neglectable for a time horizon of a few days. However, for longer time horizons the calculation time grows heavily. Starting with a calculation time of ca. 30 seconds for a time horizon of 7 days, the calculation time grows to more than 20 hours for a time horizon of 364 days. Having in mind that the case studies carried out in this thesis require a few thousand simulation runs the calculation time of 20 hours for one run is not ac-ceptable. Therefore the capacity price of every pump storage plant is analysed for different time horizons and compared to the capacity price for a time horizon of 7 days. The analysis shows that the influence of the time horizon on the capacity heavily depends on the ratio of

7 Intel Core 2 Duo E6600 2.4 GHz, 2 GB RAM, (only one core is utilized)

storage volume and installed capacity. Plants with a higher storage capacity ratio tend to cre-ate higher incomes with longer time horizons. Plants with a smaller ratio show an opposite effect which is caused by lower incomes in the summer period. In order to reduce the calcula-tion time of the model, the income ratio of the calculated capacity price for a time horizon of 364 days and a time horizon of 7 days is calculated.

Formula 5-13 Calculation of the income ratio

⎟⎟⎠

⎜⎜ ⎞

⎝

⎛

⎟⎟⎠

⎜⎜ ⎞

⎝

⎛

=

7 364

7 364

* g

p

* g

p r

i i

* i

Legend:

Variables Unit Indices

r* = Income ratio of pump storage plant p [None] i = Index of plant p*₃₆₄ = Simulated capacity price for 364 days [Euro]

p*₇ = Simulated capacity price for 7 days [Euro]

g = Generation capacity [MW]

The standard time horizon for the calculation of the capacity price on the secondary reserve market is set to 7 days. In order to reduce the error caused by this assumption, the calculated capacity price of every plant is multiplied with the income ratio determined according to Formula 5-13: The income ratio for every plant is given in the Appendix.

1 10 100 1,000 10,000 100,000

0 50 100 150 200 250 300 350 400

Days

Time in s

Figure 5-16: Impact of the time horizon for pump storage optimization on calculation time

Source: own illustration

After the closure of the secondary reserve market the remaining capacity of pump storage plants is bid into the spot market on day-ahead basis. In order to determine the load profile for the bid, the developed algorithm is utilized based on a day-ahead 24 h price prognosis. The resulting load profile is bid into the market by a price independent bid.