Influence Types of Startup on Hydrothermal Scheduling

The energy costs of a power plant consist of startup cost and cost of power usage. In contrast to the existing literature, this study introduces at startup cost based on the duration of thermal power plant downtime. The approach of startup cost function in this research is done by using startup type. Startup of a steam power plant depends on its condition. Generally, there are three types of startup the power plant when the turbine temperature is still very high, i.e. hot start, very hot start and very-very hot start. This paper uses multistage optimization to solve the problem of hydrothermal scheduling with including the startup type cost in the objective function. The simulation results showed operating cost savings when the objective function for optimization also consider the cost based on startup type i.e. when compared with the optimization result which the objective function does not take the cost of startup type.


Formulations of Reservoir Management
Simulation for optimization of the energy costs in the hydrothermal system, the first stage is done with maximize using of water. Maximizing the use of water can use the following constraints and functions, as shown reference [1]. Equations (1) through (7) are taken from reference (1). The first constraint, Where, , = . (2) The second constraints are, For water management will use the volume of water at the hour at = that is equal to or smaller than the volume of water reservoirs at = , namely.
Where =25 is calculated as an optimization constraint condition, whereas =1 is a constant defined based on previous optimized results or defined as initiation. So the objective function of the problem is expressed by in Equation (5). With, While weighting value for the energy cost can be expressed by Equation (7). 24 (7)

Formulations of Power Plant Startup Costs
Startup costs depend on duration a power plant has not connected to the grid or downtime duration. The downtime duration for short time scheduling hydrothermal is grouped into 4 conditions. That is the current condition ( ,0 ), the condition of one hour earlier ( ,−1 ), the condition of two hours earlier ( ,−2 ), and the condition of three hours earlier ( ,−3 ). So the startup costs can be expressed as follows.
Two important conditions to identify those startup costs are the current conditions and the previous conditions. Namely, when ,0 = and ,−1 = 0 then there will be startup costs. Then startup types expressed at the time = − and = − . Detail conditions of the startup type can be described as follows. Other conditions that need to be considered is the condition of no startup costs. That is, when ,0 = 0. This condition is called power plant disconnected from the grid. Furthermore, without the cost of startup is when ,−1 = and ,0 = . That is the condition of the power plant is still connected to the grid.

Formulations of Hydrothermal Costs
The objective function of energy costs optimization is: ∑ ∑ ( , ) =1 24 =1 (9) With N is total number of power plant, and ( , ) is: ( , ) = , × ( , ′ + + . , + . , 2 ) With α, β, γ are the parameters cost which depends on the type of power plant, as shown in  [21]. Symbols subscript x is a power plant that is cost at the time j. Then ( , ′ ) are startup type cost for each power plant.

Formulation of Power Plant and Grid Constraints
Furthermore, to optimize the use of power on the grid will require the formulation of constraints such as power constraints, voltage, and phase angle. The constraints on the electrical system refer to the paper written by Zimmerman [2]. The constraint consists of constraint Equations and inequality constraints. The equation constraint consists of the active power equation and the reactive power equation on each bus of the electrical system being reviewed. The inequality constraints consist of maximum and minimum voltage constraints, maximum and minimum phase margin constraints, active and maximum reactive power limits, as well as minimum and maximum reactive power on power plants.

Algorithm Optimization
Modification of the multistage algorithm from reference [1] will be done with the following steps.
1. Optimization begins by maximizing the use of water in hydropower plants. Maximizing the hydroelectric performed to determine the amount of the power plant that will support the grid, and determines the amount of power generated by each unit. Maximizing done for every hour in 24 hours of operation. In this first stage will get a number of power plants and the power to be supplied to the grid for every hour of operation.
2. Then, the selection of the thermal power plant will be connected to the grid. Selection is done by using economic dispatch without computing grid constraints. I.e. by using evolutionary algorithms contained in the solver spreadsheet to minimizing the cost of power generation by determining the power plants that will commit operation for every hour. Included in this calculation are various types of startup costs. To ensure that stages of the optimal power flow (algorithms stage 3) can be done very well, at this stage of economic dispatch, the estimated load is set to increase by approximately 2%.
3. Next step, there will be optimization of power flow. Simulation of optimal power flow will use an interior point method. Optimization of power flow, it will generate optimal of power from each power plants that will be committed for connected to the grid at each hour of operation.
4. With simulation results of optimal power flow, and then inserted into the spreadsheet that is to calculate the overall energy costs including startup costs. Flowchart of the optimization algorithm as shown in Figure 1.  As a comparison calculation, optimal power flow calculation will be done using the decommitment units interior point solver to obtain the thermal power plants to be connected to the grid at every hour of operation. After that, the same with a step 4 on multistage optimization, the results of the optimization of the power then inserted into the spreadsheet that is to calculate the total energy cost including the startup cost.

Simulation and Results
Simulation algorithms for scheduling hydrothermal system have been described in the section above. The data in the following tables will be used to support the simulation. The Table 1 and Table 2, an electrical system data, that are taken from reference [1].   The line that forms the grid is described as a connection from f bus to t bus with specific of resistance (r), reactance (x), and Susceptance (B). Branch data between the buses on a grid shown in Table 2.
Furthermore, the first stage is simulated to optimization for maximizing the use of water from the reservoirs.  . The minimum water reserve for the next day is 10 x10 6 m 3 . The minimum water limit that can be used is 5x10 6 m 3 . This simulation is done to maximize water use for the dry season, i.e. when the water supply is limited. Namely, with input for the upper dam about 60 m 3 /s. The lower dam gets input from the upper dam and additional inputs from tributaries about 3 m 3 /s. Maximizing the use of water is done by calculating the load data grid for a duration of 24 hours. This data is used to perform a weighted value for the use of water in a hydroelectric power plant. Optimization is based on the weighted value of the service load from the hydrothermal systems. The optimization results are shown in Table 5.  Finally, the optimization results have been obtained that all units can be connected to the network on the hour from 19.00 to 20.00. It was consistent with the fulfillment of peak load for the grid. Power generated by each unit, shown in Table 5. The minimize costs i s done by selecting the power plants and the power must be supplied to the grid at every hour of operation.

Minimize the Energy Costs
Minimize costs will be performed by the economic dispatch. It will be used to select power plants that will be connected to the grid at certain time duration. Type of startup cost for thermal power plants will be done with the assumption that cost is comparable with the energy costs of a minimum power generated then multiplied by a constant. Constants will depend on the startup type whose value is as follows.
1. The very-very hot start will be multiplied by one.
2. The very hot start will be multiplied by two.
3. The hot start will be multiplied by three.  Notes for the implementation of the economic dispatch optimization using a spreadsheet solver are as follows. If the cases with a large grid and due to limitations of optimization ability on the spreadsheet solver, then at the stage of selection of thermal power plants that will enter the grid for 24 hours taking into account the type of startup can be done by dividing into 3 groups of optimization sequences or larger. So each group consists of 8 hours or less, depending on the spreadsheet solver. And, the three hours of optimization results on the previous day can be used as an initiation of economic dispatch.
Economic dispatch results then are given by the input to determine the optimization of power flow. Power flow optimization will get power every hour from every power plant serving the grid. The result of each step of the optimization is shown the Table 6.
In this comparison, the first step is to take the maximum water use outcome. Then, power flow optimization is performed using interior-point solver with the decommitment unit (DC-IPS) for every hour of operation for 24 hours. The results optimum power flow were as shown in Table 7 Table After the optimal data obtained from the optimization of power flow on Table 6 and  Table 7 above, then calculated energy cost by entering the power data to the spreadsheet. The spreadsheet in their calculations includes the cost of each type of startup. The energy cost calculation by considering the cost of each type of startup is in Table 8.

Scheduling of Maximization Water Usage
Scheduling of hydro power plants (HPPs), is done by maximizing water use. In the simulation to maximize the use of water, it has been found that in the dry season the water discharge to less than nominal input, then the water will be optimal when used to meet peak load demand. It is also suitable for the fulfillment of the power capacity when peak loads. In this simulation, peak load is from 18.00 to 21.00. Optimization results have been shown in Table 5 above. Table 5 shows hydropower plant based on maximization of reservoir water use, the power plant is prepared to enter the grid during peak load hours. If the water is still suffici ent to be used i.e. at the value of a considerable weight value then the HPPs unit is also possible to be prepared.
Maximizing the use of water in the dry season turned out to be useful for the fulfillment of the overall grid system. From the simulations, it has been found that the fulfillment of the peak load by HPPs, make the grid system capable of meeting the needs of the load for 24 hours. This is shown in Table 6 and Table 7 above.

Scheduling Economic Dispatch of Thermal Power Plants
Optimizing the use of primary energy in hydrothermal systems, especially at the minimization of thermal power generation costs, consists of two stages of optimization. The first is a thermal power plant scheduling that is prepared for connection to the grid with consi deration to minimum energy costs as well as minimum startup costs based on startup type. The result of this scheduling is a generator prepared to support the electrical system in every hour of the operation plan.
In the step of maximizing the use of water for hydroelectricity, the result is the status of the generator at every hour on the daily operating plan. In the economic dispatch step during the daily operation plan, the result is a thermal power plant that does not serve the load on every hour of daily operation plan. Scheduling at the economic dispatch stage is the status of a thermal power plant at each hour of the daily operating plan. At this stage, the power of any planned thermal power plant unit has not been optimized. The economic dispatch res ult status seen in Table 6 is a thermal power generating power whose value is equal to zero (0). This indicates that the power plant is removed from the grid of the electrical system. Because at this stage optimization is done by using economic dispatch t hen the next consideration is to determine the actual power needs in each power plant that supplies the grid system. Thus, the next calculation can be done with optimal power flow, i.e. by finding the minimum value of energy cost in each hour of operation plan for each plant that has been selected.

Optimization Energy Costs
Optimal power flow is the optimization of electric power that is easy to do when using the objective function in the form of deterministic function. That is, in equation (10) with the previous two steps we have obtained the value of each binary variable ( , ), so that the optimal calculation of power flow with deterministic function can be done with conventional algorithm.
In the previous two steps have been known the status of each power plant at every hour of the daily operating plan. From this step, in equation (10) has been known every value of binary variables, so the cost function equation has become a quadratic deterministic equation. The quadratic deterministic equation can then be optimized by optimizing the power flow. A fast and accurate way to optimize power flow with a deterministic objective function form and a single variable of its methods is with an interior point. This power flow optimization is done hourly from daily operating plans. The result is an optimum power rating every hour on each power plant that is planned to support the electrical system on a daily basis.
Optimization results of optimum power flow calculation with interior point method is in Table 6. Table 6 shows the optimal power value of multistage algorithm. The power value in Table 6 is the optimal power value generated by the multistage algorithm taking into account the startup type cost of each power plant.
Then as a comparison of the multistage algorithm will use the de-commitment algorithm of interior point solver unit to determine optimal power from the thermal power plant. The power generated at DC-IPS is shown in Table 7. When compared to Table 6 and Table 7 that is the thermal power plants, it is seen that the decommissioning unit to serve the load demand both types of optimization do so on different generating units. In the interior point method more CCP 5 to CCP 10 and CCGT are often removed from the grid. While the DC-IPS method turns out CCP 5 to CCP 10 is more used to serve the grid.
Thermal power plants in tables 6 and 7 in the scheduling have different results. That is, Table 6 has shown that the tendency the power plants to always serve the load if the power plant has been connected to the grid system. It is intended to avoid the startup costs with greater costs if the power plant to be colder. The result to be different when the optimization without the startup costs, as shown in Table 7. Table 7 that is in CCP 14, since it does not consider the startup cost type in its objective function it becomes activated at the 10th and 11th hour to replace CCP 13. Differences in the selection of status and power in both methods resulted in different optimization of generating costs.
Based on the power generated, the use of interior point algorithm without the startup type costs included in the objective function, the result was a bit more efficient. It has been shown in Table 8 in column 3 and 5. However, Table 8 in column 4 and column 6 has also been found that the calculation of the cost turns out to be a bit cheaper when the startup type costs included in the objective function.

Conclusion
In the hydrothermal system, during the dry season due to the limited water, maximize the use of water has become a priority to fulfill the peak load. The simulation results with modification of multistage algorithms for a minimization costs by engaging the startup type has been shown more effective results when compared with optimization without involving the startup type. But for power flow calculation, the results of the simulation with startup type showed relatively little more spendthrift. Thus the use of startup types on energy cost optimization for hydrothermal systems is better when included in the optimization algorithm. Startup costs with account of the startup type for unit-x, at a time j P Di Active power of the load on bus i P Li Active power flow through the line from bus i to k P Gi Active power generated by the power plant on bus i θ ik = θ i − θ k Phase angle difference between bus i to k G ik Conductance cable from bus i to k B ik Susceptance from bus i to k