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Short term power system planning with water value and energy trade optimisation

Marin Cerjan#1, Danko Mar�i�#2, Marko Delimar*3 #HEP Trgovina d.o.o

Ulica Grada Vukovara 34, Zagreb, Croatia 1 [email protected] 2 [email protected]

*University of Zagreb Faculty of Electrical Engineering and Computing

Unska 3, Zagreb, Croatia 3 [email protected]

Abstract—This paper emphasises the importance of a well planned unit commitment model in coordination with water value evaluation to achieve optimal economic results for genco. The existing water value models are examined and customized for the developed power system model. Linear programming methods are used to achieve optimal economic performance for hydro and thermal power plants production and the power exchange is calculated. Several scenarios of short term planning with emphasis on water value and power market exchanges are presented. Index Terms— water value, economic dispatch, power system planning

I. INTRODUCTION

Electricity utilities have been undergoing radical changes with process of deregulation and changes in their market and regulatory structure. Basic idea is to promote competition on energy market which should lead to lower prices and result in higher investment and technology progress. In most cases, the restructuring process has replaced traditional expansion planning and operation procedures based on centralized optimization by market-oriented approach.

Today, many different models can be found in power system planning which are classified according to the planning horizon. Long-term planning models deals with investment typically over a 15-20 year horizon. Medium term planning is done over 1-3 year range and deals with reservoir management, while short term planning which deals with problems such as consumption forecasting, unit commitment and economic dispatch has horizons of one month or shorter. [1]

Decision making in the energy sector has to be based on accurate forecasts of the load demand. Forecasts of different time-horizons are needed for the operation of power plants while the system response follows closely the load requirement. Most developed is short-term forecast which is influenced by the weather conditions, seasonal effects and the

day of the week. There is a common agreement that the air temperature is the most important weather influence [4]. This correlation for the Croatian power system model is illustrated in Fig.1.

Fig.1. Daily consumption and average temperature for the Croatian

power system model There are many methods in short-term forecasting such as classical time series and regression methods [2] time series models [3], artificial intelligence and computational intelligence methods [4] hybrid and other approaches [6]. Performance of a certain method can be evaluated by absolute mean percentage error (MAPE) where yt is real value at time t, ft forecast at time t of period T. MAPE for some advance models is lower that 2 % .

1

100 Tt t

t t

y fMAPE

T y=

−= � [%] (1)

Economic dispatch is the process of allocating the required load demand between available generation units and energy market such that the cost of operation is at the minimum. It is usually used in combination with unit commitment and hydro-thermo coordination.

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2011 8th International Conference on the European Energy Market (EEM) • 25-27 May 2011 • Zagreb, Croatia

978-1-61284-286-8/11/$26.00 ©2011 IEEE

Water value can be determined with variable cost of power system production and market price. It's usually defined trough marginal cost under given time interval as alternative value for reducing production of thermal power plants or energy import. [14]

For last few years we have witnessed high price volatility on EPEX which appears primarily from increased share of renewable energy source, especially wind. Problem in planning of wind production is to estimate the moment in which the wind will appear, and with a large share of installed wind power, large energy production in short time period can create big impact to the energy system, making energy surpluses which usually end on power exchange. Increase of wind production can reduce electricity prices on energy exchange, as shown in Fig. 2. This is more significant [11] in systems which have a high proportion of thermal unit that are characterized by high cost during the suspension. In circumstances of high wind power production it is cheaper to sell surpluses on energy exchange (even for negative price for few hours) that suspension thermal production facility.

Such situation gives great opportunity for flexible power system such as Croatian to reduce hydropower on days with low energy price to buy energy, and to increase it again in days when the price of electricity is high. Because of the high liquidity on EPEX it is always possible to trade physical energy due to the good connection over auction office for allocation transmission capacity.

Fig. 2. The impact of wind power on the spot power price in the West

Denmark power system

II. EXISTING WATER VALUE MODELS

Operating cost of each thermal power plant depends

basically on its fuel cost. Therefore, thermal plants are represented by their unit operating cost {cj, j=1,...n} (�/MWh) and their generation limits: �� for j=1,...n (3) where: �� - maximum generation capacity of plant j

The scheduling problem is to determine the power plant combination that minimizes the total fuel cost required to meet the system load

� ! "#$% �&��'�()*+ (4)

subject to , ��()*+ �� ! �� (5) �� (6)

z(t), c, d(t), g(t) and g represent respectively the system operating cost in stage t, unit operation costs, system load, power production and generation capacities. Hydro power plants can use the energy stored in their reservoirs avoiding fuel expenses with thermal unit. The availability of hydro energy is limited by reservoir storage capacities. The major decision point in hydro scheduling is to release water in such way that the immediate financial gain equals the expected future value of water. The expected future value of water is presented as a function of reservoir level, present inflow and time. Water value is a long-known concept that dates back to 1960s developed for Swedish power system [7][8]. For hydro planning problems stochastic programming has been used for a long time. First models were developed in early 1980’s.[15],[16] Pereira presents his model of hydro operation cost as a function of future reservoir level Fig. 3. The immediate cost function ICF is related to thermal generation costs in stage t. As the final storage increases consequently and less water is available for energy production in the stage, as a consequence, more thermal generation is needed, which increase the immediate cost. In turn, the future cost function FCF that is associated with the expected thermal generation expenses from stage t+1 to the end of the planning period, is low because more water will be available for the future cheap hydro generation.

Fig. 3. Immediate and Future Costs versus Final Storage

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The FCF is calculated by simulating system operation in the future for different starting values of initial storage and calculating the operating costs [16]. In a deregulated setting, spot market price becomes important input to power scheduling models. Optimization problem gains a new dimension while system is scheduled in accordance to market circulation. A generating company basically has no other objective than to produce electricity at a low price and sell with maximum profit. This leads to the following problem: how to forecast future market price but also at the same time follow proper reservoir management? In the Norwegian case analysis of the price scenarios it is shown that the market price for each week strongly depends on the price in foregoing week. In order to use an optimization algorithm based on dynamic programming one of models is to use simple autoregressive model. [13], [14]

-.��/ 0 1� ! 23��/�-4�/� 0 5�/� (7) -.�� 6��78 -4�/� ��9�� 6��-.�� 23��/� ��:��9�� 9�� 5�/� ��9��9�6��;�

III. SIMULATED POWER SYSTEM MODEL

In this paper observed power system is modelled after

Croatian with all the necessary similarities. Balance ratio between hydro and thermal production is proportional. Permanent economical development and increased consumption throughout the last 20 years was not followed by the appropriate deployment of new power generation utilities which resulted in raising demand for the electrical energy import that has reached roughly 30 % of total energy consumption, according to the UCTE [17].

For the simulation purpose of price model calculation, imaginary power system will be observed that has similarity with Croatian power system in the way it is shaped in approximately 50% decreased compared to the real one. That system will consist of six hydro power plants and five thermal power plants presented in Table 1.

Prior all the necessary calculations are performed the plan’s objective has to be established by creating the global medium-term plan for year ahead power system performance. The principal of plan making is well settled approach that has proved to be successful through the years achieving best engineering and economical performances out of the power system. Due to the large share of hydro power plants, power system optimization depends a lot on the weather events and the amount of precipitation, so the most important is future reservoir water inflow. Since there are no accurate weather forecasts for period of one year all forecasts are based on statistical evaluated data for last 30 years. On the basis of processing and analysing historical data come the results which are described in three possible scenarios. These

scenarios describe events with approximately 30 % possibility of large and low water inflow, and the statistically the most possible event as well.

TABLE I CHARACTERISTICS OF GENERATION UNITS USED IN THE SIMULATED POWER SYSTEM

Name Type Fuel Min Power [MW] Max Power [MW]

HPP1 Run off Hydro power plant Water 8 50

HPP2 Hydro power plant with reservoir

Water 35 215

HPP3 Hydro power plant with reservoir Water 10 20




TPP1 Thermo power plant Crude Oil 110 250

TPP2 Thermo power plant Crude Oil 100 180

TPP3 Thermo power plant Gas 20 50

TPP4 Thermo power plant Nuclear 250 400

TPP5 Thermo power plant Coal 110 190

Generation of hydro power plant’s and reservoir management are defined, as well as thermo power plant production and energy exchange at the end. Croatian power system is throughout the most part of the year exposed to power exchange. This comes from the characteristics of energy consumption curve where the difference between minimum and maximum hourly load can be close to 100 % which requires a large scale of flexible production capacity. Short term system planning applies from day to month system planning. Through this part of the planning middle-term planned dates are corrected regarding accurate weather forecasts for energy consumption and weather evaluation as well as the market fluctuation for coming time period

IV. CALCULATING WATER VALUE

When assessing the cost of production it is necessary to

define fixed and variable costs. Their individual significance is depending on the proportion of each cost. That means, with increase of utilized capacity fixed cost are declining and variable increasing. This pattern in theory of costs is known as “the principle of mass production” and is expressed with following formula. [18]

�< ! =>? 0 @< (8) 7�� A�total average cost�BC�A�total fixed cost�D�E�production quantity�6��A�total variable cost� Variable cost of thermo power plant is characterised by a

specific heat rate curve which defines necessary heat energy

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for producing one unit of electrical energy H(P). Multiplying it with power produced, fuel price coefficient and fuel caloric value the fuel cost curve C(P): F�G� ! H3 0 I 0 JG�� K LMLNOP (9)

Q�G� ! G R F�G��KSMO P (10) T�G� ! / R Q�G� ! U 0 VG 0 <GW �KXOP�� (11)

where G ��9��7�� 2Y IY J ��:�� Q�G� �� 6 T�G� �� / ��:��

Additional costs such as start up allocation, fuel limits allocation or environmental cost of polluting can be also involved in function cost coefficient making them dependable on produced energy. Water value is calculated deterministic with function fc (P) shown in Fig. 4.

Z[�G� \]^�� ! ]3^��Y Z[�G� ! _]^�� ` ]3^��Y Z[��G� ! a]^�� b ]3^��Y Z[�G� ! c d

(12)

where: Z[�G� ��6��7��6�� G ��7�� 9 ]^ ��6��6� ]3^ ��6��6� If system requires additional power P, it can be bought from market, produced from thermal power plant or produced from hydro power plant with reservoir. Optimal production is projection of long-term reservoir management planned and forecasted inflow balanced with thermal power plant production. In ideal case where planned reservoir level is equal to real reservoir level water value is equal to minimum replacement value of thermo power plant or average market price for last 5 days.

Fig. 4: Water value in dependence of reservoir level and water inflow

In case of under plan, price is higher and in case of over plan price is lower. Water value is evaluated for base load, which means that the water value is same for all 24 hours a day. This gives an option to produce energy only in peak hours which are the most expensive on energy market. Simulated hydro power plans reservoirs have an annual cycle. There is a very intensive hydrological period (early winter and late spring) which is ideal for filling the reservoirs, and dry hydrological period (late spring to late fall) during which stored water can be used for additional energy production. Price of produced energy from run-off hydro power plants is calculated separately. Water inflows that occur must be used immediately or in a very short time because usually continues flow plants have daily flow reservoirs. If the inflow is lower that max these power plants can be optimised by producing energy in the most expensive hours. In simulation model, continuous flow power plant have daily reservoir capacity not bigger than maximum daily production of power plant. After setting prices for energy production for simulation model next step is system production optimization. For power plant optimization, linear programming is used with duration load curve for hourly optimization of power plants production. Linear programming is an optimization procedure that minimizes a linear objective function with variables also subject to linear constrains. In this case the objective function that gives the best representation of observed problem is: e#$ ,<��f�� 0 ,g�/Y @fh+� 2fh+�/�@fh+�/� i jk (13) where: e#$ ,<��f��99��9��7�� Operating cost in stage t ,g �/Y @fh+�2fh+�/�@fh+�8� � ��7�� ; l g�/Y @fh+� ��:��6��/ 2fh+�/� 7��6��6�� @fh+�/� ��6��6��9�� jk ��7��m�� This function could also be written in more simplified way in order to be more under stable: 9�� Q ! , <k�nGG� 0 , <k�FGG� i <�Gjo�pk*+qk*+ (14) where <k�nGG� ��9��7��# <k�FGG� �� 7��# <k�Gjo� �� ;��7��m��

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Certain constrains that have to be taken into account are: <k�FGG� ! gk r sfh+ (15)

Where gk� represent, such as in formula, (13) production coefficient of reservoir i after time period t. This value has to be smaller or equal as the desirable stage of the reservoir i after the period of time ��sfh+�t�This will result in optimal water value based on stochastically assumed inflows after each computed period of time. , <k�nGG� R Gk 0 , <k�FGG� R Gk i <�Gjo� R G ! upk*+qk*+ (16) Equation (16) states that at each period of time sum of power production and energy exchange has to be equal the planned load. The optimization criterion that has to be satisfied in order to achieve the maximum financial output from system is: <k�FGG� 0 <k�nGG� � 9��v<�jGjo�Y <k�nGG�w (17)

V. SIMULATION RESULTS

All calculations and forecasts are simulated in Microsoft Excel using Visual Basic and Solver function for linear programming.

It is important to emphasize the limitations which are used during simulation:

• for run-off hydro power plant all daily inflow is used for production at the same day

• all hydro plants with reservoir are not combined in cascade

• error of daily load forecasts and water inflow is negligible

• import is limited to 500MW • export is limited to 500MW • nuclear power plant is planned to run all the time • no limitation in power grid

Here are presented simulation results for two specific cases through year. First is simulation for forth week of 2009 in which the hydrology was very strong and the reservoir level high through longer wet period before that. In second case reservoir level is a 6% lower than planned and the water inflows were lower that planned. Here is shown the full potential of water value optimization.

A. Case 1 - Winter period

First simulation was made for period from 19.1.-25.1.2009. As mentioned before winter 2008/2009 was rainy from the beginning of the December so the reservoir level was very high at the observed period. Interesting for that week was high increase of inflows which at the peak on 24.1 were 200 % higher then planned. Storing additional water was impossible considering the current reservoir level in correspondence with statistical raising inflow prediction

Fig. 5. Simulation result for Case 1

All this circumstances affected the water value which were lower that energy exchange so hydro power plants were planned for maximum production and all surpluses were sold on market, Fig. 5.

B. Case 2 - Summer period

Second simulation was made for the period from 13.7.2009 to 19.7.2009. Energy consumption was high, reservoir level 6 % lower than planned and water inflows 50 % lower than plan. This was very hot and dry period of the summer. Consumption was high not only in Croatian but whole Europe so the energy prices were rising for this whole week. Calculated water value was greater than average base load but lower that peak hours. That principle leads to buy cheaper energy on energy exchange for first three day and to produce maximum at our peak load. Also high price weekend on power exchange create great opportunity for system to produce addition surpluses and sell it on power exchange and to compensate high volume which were bought for first three days. Results of simulation are shown on Fig 6.

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Fig. 6. Simulation result for Case 2

Results for Case 2 are quite interesting because system performance and management during this time in reality was done different considering the high consumption and statistically predictable dry period.

VI. CONCLUSION In this paper the formulation of water evaluation model for

hydro power plants with accumulation was presented. Water value was evaluated for every day separately taking into account long term plans for reservoir management, prices of other power plants in the system and prices on energy exchange. Estimation models for water evaluation have been developed quite intensively over the last twenty years and their implementation significantly varies depending on the unique geographic position of each country, its production capacities and energy exchange accessibility.

This leads to liability, where with flexibility of hydro power plants production, price volatility on power exchanges can be used to make a great economic benefit for an energy company. This is best shown on Fig 6. Simulations were made on simplified model of the Croatian power system, and satisfactory results were obtained for hydro-thermo

coordination with a goal to achieve optimal economical performances of the simulated power system. It is interesting to note that this kind of market oriented behaviour is very untypical for conservative and monopolistic power system such as Croatian whose primarily goal is still minimizing the operating costs.

It is important to mention that all simulations were done on a simplified model in order to achieve achievable computing performance time. For further calculations it is possible to implement a more realistic system topology with cascading hydropower plants whose water balance is fare more complex considering the inflow delay time, or more detailed modelled reservoirs that are perhaps permeable. This would require an application of a new simulation model for cost analysis because the number of constrains and new parameters would increase.

When applying this model on a real systems, system specific parameters based on system specific technical characteristics should be taken into account as well as environmental and socio-economic limitations.

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