Optimal Operation Of Wind Psp

Published Date: 02 Nov 2017

Abstract - This study is carried out on the problem of short-term Wind - Pumped Storage Plant (PSP) scheduling under the Grid connected day ahead market. A mixed integer nonlinear programming approach is proposed for scheduling the generation efficiently. The proposed approach maximized the profit across the day ahead market by optimizing the Wind-PSP output generation to supply the consumer demand at given market price, where wind data has been forecasted for day ahead scheduling. The imbalances in the forecasted wind data and the market demand have been reduced by operating the pumped storage plant with the wind turbine. The reliability of this approach has been further improved by replacing the conventional pumped storage unit by the adjustable speed type pumped storage unit. Two case studies have been considered to prove the optimality of the solution. In first case study scheduling provided by operating the conventional pumped storage unit, whereas in second case study, adjustable speed pumped storage unit has been used. This unit has further reduced the imbalance between generated power and demand. Complete approach has been formulated and implemented using AMPL.

Index Terms— Wind Energy, Pumped Storage, Optimal Scheduling, Optimization, Deregulated Market.

INTRODUCTION

During the nineties decade several nations like U.S., U.K., Spain Norway started to deregulate and privatized their power markets [1]. These markets run by Independent System Operators (ISOs). Several auction organized by the ISO where utilities could buy and sell power between them. Energy producer participate in these auctions by submitting their energy bids. The ISO collects these energy bids and combines them with energy bids from the consumer to construct the aggregate supply and demand curves. The ISOs use optimization algorithm techniques to allocate these energy in such a way so that it increases overall profit. Under the new market structure, an energy producer sells electric energy into the market through integrated resource bidding and scheduling. After the market clears, the energy producer has the obligation to provide scheduled energy on an hourly basis based on its accepted bids. The producer may be penalized if the scheduled energy delivery cannot be realized.

This paper provides the combined operation of wind and pumped storage plant with the grid connected deregulated power market, which supplied the generation according to the demand or bid provide by the market. One of biggest problem related to operation of wind power plant in the electricity market is its high penetration of variable generation, which tend reduced the reliability as well as the profit across the market. In order to fully utilize potential benefits and to minimize adverse impacts of wind energy, it is required to integrate the wind power energy with various dispatchable energy sources like hydro, Thermal etc. In [2-6] various researchers provide great attention toward the energy storage devices for reducing the impact of wind energy like Flywheels, battery storage etc. but these devices only used in the wind farm of small sizes. For the large size wind farm pumped storage plant is used which is one of the technically mature and economically viable alternative. Pumped storage plant (PSP) is the oldest kind of large-scale energy storage technology. This is superior to other energy storage technology because of their operational flexibility and ability to provide rapid response to changes in system loading or spot price of electricity. However, in conventional PSP, pumps only operate at fixed speed, so input power adjustment during pumping is not possible. One of the recent remarkable developments in PSP technology is evolution of adjustable speed units in which it is possible to change the speed of pump. This further improves the reliability of the power system and may enhance the competitiveness of PSP in deregulated power market [7].

In conventional pumped storage plant [8], a salient pole synchronous motor-generator is coupled either to a separate pump and turbine or to a reversible pump turbine. The arrangement can be horizontal or vertical. Because the rotational direction of a separate pump and turbine arrangement is the same in both operation modes, this setup allows for a more rapid change from turbine to motor operation mode or vice versa. It is however more complex and leads to longer shaft arrangements resulting in higher costs, especially if the power station is located in a cavern.

In variable speed power plant, static frequency converters are used to vary the speed of the electrical machine [8-9]. For the small unit approximately less than 50MW, conventional synchronous generators is used with a static frequency converter but for larger units, this solution would be more difficult to justify economically. For units larger than 50MW, double fed induction machines with a static frequency converter feeding the rotor are the preferred solution. This became possible by exciting the rotor with low frequency alternative current with the help of converters. In first realizations of variable speed pumped storage projects, Cyclo converters were used to create the rotating field on the rotor. Cyclo converters are direct converters and, consequently, absorb reactive power. This power needs to be compensated by condensers or provided by the generator. Furthermore, the frequency range of such converters is limited. They cannot be used to start the unit in pump mode, which means an additional static frequency converter needs to be used to start the unit. Cyclo converters using Thyristors are a robust technology proven for many years. More recently, improvements in the power ratings of IGBTs and IGCTs allow for the construction of large voltage source inverters. These converters do not absorb reactive power. Furthermore, they can be used to start the motor in pump mode. For this purpose the stator is short-circuited and a rotating field of increasing frequency is injected into the rotor. These converters provide the frequency or speed variation of plus/minus 5 to 8% which control the input power of pump by approx. 60 to 100 %.

In this paper, both wind and pumped storage system are operated as single entity, which are not necessarily installed at the same or adjacent location. PSP considered here, consist of reversible turbine unit which can ether generate or pump the water according to requirement. Both of the systems (wind and PSP) are connected with the grid. A certain strategy is used in this paper, which efficiently utilized the power generated by wind and PSP according to the demand or bid taken from the market. In this strategy, energy generated by the wind power plant is stored via pumping action during the low demand period and stored the energy in upper reservoir. For utilizing the wind power variation in effective way as well as to reduce the imbalance in market, PSP offer variable speed during the pumping mode. In this approach, wind energy has been forecasted for day-ahead market. This wind and pumped storage scheduling problem is formulated as a mixed integer nonlinear programming problem and the optimality of solution has been proved by considering the two case studies. In first case study scheduling provided by operating the conventional pumped storage unit, whereas in second case study, adjustable speed pumped storage unit has been used, this further reduced the market imbalances created by wind turbine and market demand.

Problem Formulation

In this problem, MINLP approach is used to determine the optimal hourly scheduling of power generation by wind and PSP. These entities operate in deregulated power market to increase the overall profit.

Objective Function:

In market based system, the revenue or profit of the PSP is maximized by operating it as generator when the market clearing price (MCP) is high and as a pump when the price is low. The income of a PSP includes net revenue received out of selling energy in the day-ahead market when it is operating in the generating mode and buying energy when it is operating in pumping mode. The objective function for this problem has been formulated to maximize the market profit by optimizing the combined operation of pump storage and wind farm as given in equation (1). This objective function consists of the revenue of pump storage plant Rpsp(t), wind farm Rwind(t) and the revenue loss due to the imbalances Rloss(t).

Maximize: (1)

Where:

(2)

(3)

(4)

(5)

(6)

Equation (2) determine the profit of PSP at tth hour where Rgen(t) is the revenue of the PSP during generating mode and Rpump(t) is the revenue of PSP during pumping mode. Revenue of the power generated by PSP Rgen(t) is defined as the product of the power generated by PSP Pgen(t) and the market price mkt(t), where s(t) is the switching variable for generating mode as given in equation (3). During the pumping mode the PSP uses the power from two sources wind farm and the grid. The total revenue during the pumping mode is the sum of revenue from the generation by wind farm and the grid as given in equation (4). Where wind is the price paid by the PSP to the market for utilizing the wind power for pumping operation, This remains constant for whole period. Rwind(t) in equation (5), is the revenue generated after supplying the power Pwmkt(t) to the market by the wind farm. Rloss(t) is the revenue loss or the penalty imposed by the market for creating imbalance between generation and demand as given in equation (6).

Constraints:

Above objective function has been formulated subjected to the following equality and inequality constraints:

Grid Pumping Limits

In this approach, wind-pumped storage system is connected with the grid to supply the pumping power to the pumped storage plant. The power supplied by the grid for pumping has upper and lower limit, which is given in equation (7).

(7)

Wind Power Constraints:

The total power generated by the wind farm is Pwgen(t). During its operation it is not possible to utilize all the power generated, some power may remain unutilized. This power is determined by the constraints as given in equation (8).

(8)

Where Pwpump(t) is the power consumed by the PSP during the pumping mode, Pwmkt(t) is the power taken by the market and Pwun(t) is determined the unutilized power.

Pumping Constraints:

For the pumping operation the PSP can take the power from the grid or wind farm, which is given by the equation (9).

(9)

Where Pwpump(t) is the power consumed by the PSP from the wind farm and Pgpump(t) is the power consumed by the PSP from the grid. Pp(t) is the power consumed by pump during pumping mode. sp(t) is the switching variable for pumping mode.

Imbalance Constraints:

In equation (10), Rloss(t) represents the total imbalance in the market, which implied that the total generation provided by the market is always equal to or less than the total demand across the market.

(10)

Energy balance Constraints:

The equation (11) determines the energy balance in the upper reservoir.

(11)

At the beginning of (t+1)th hour the energy in the reservoir E(t+1) is the sum of initial energy level in the reservoir E(t) at tth hour, is the energy supplied to the reservoir during pumping mode and is the energy used from the reservoir during generating mode, whereas s(t) is a control variables. td is the time deviation. and are the efficiencies of pumped storage plant during pumping and generating mode respectively.

Reservoir Limit

The energy stored in the reservoir has upper and lower limit and is given in equation (12).

(12)

Here, Emin and Emax are the minimum and maximum energy level in the reservoir.

Reservoir level

In this formulation it is assumed that the initial and final level of the reservoir is equal to each other so that stored energy can be utilized in future for scheduling.

(13)

Generator Limit

This constraint keeps the power generated by the pumped storage plant within the upper and lower limit, which is given in equation (14). Where the and are the minimum and maximum power generation limit of pumped storage plant.

(14)

Pump Limit

This constraint keeps the power consumed by the pumped storage plant within the upper and lower limit, which is given in equation (15). Where the and are the minimum and maximum pumping limit of pumped storage plant.

(15)

Switching Constraint

This constraint controls the operation of PSP between the generating and pumping mode and do not allow both the operation same time as given in equation (16). Where s(t) and sp(t) are the control variable of pump storage plant during generating and pumping mode.

(16)

Control Variables

A control variable s(t) is used in this formulation as given in equation (17). This variable controls the operation of PSP in generating mode. Whereas sp(t) is the variable which control the operation of PSP in pumping mode as given in equation (18).

(17)

(18)

Solution Technique

In this study, mixed integer type problem is formulated in the AMPL by using KNITRO as a main solver [10]. This solver mainly used for finding local solutions of different type of optimization problem with or without constraints. It provides the efficient and robust solution of small or large problem. In this problem, a Mixed Integer Nonlinear Programming (MINLP) is used by the KNITRO for providing the solution. The KNITRO mixed integer programming (MIP) code offers two algorithms for Mixed-Integer Nonlinear Programming (MINLP). The first is a nonlinear branch and bound method and the second implements the hybrid Quesada-Grossman method for convex MINLP. The KNITRO MINLP code is designed for convex mixed integer programming and is a heuristic for nonconvex problems. For this problem, convex MINLP is using a nonlinear branch and bound method for finding the optimal solution.

RESULTS And Discussions

The considered Deregulated market includes Wind power plant of 380 MW and a single unit of pumped storage plant with 59.65 MW capacity. The market time horizon is 24 hours. Two case studies have done to prove the optimality of the solution. In both cases reversible type turbine used which operates in both pumping and generating mode. In 1st case study the conventional pumped storage unit run at its rated power during pumping mode, where as in the second case pumping input power varies between two different values for adjustable speed type unit which further reduced the market imbalances Data for PSP unit are based on Hiwasse Dam unit-2 [11] and are detailed in Table – I. In this table mode of operation indicates the operating mode of PSP’s turbine. For both case studies the initial and final level of the upper reservoir is assumed to be equal so that it can be utilized for next day scheduling as given in Table II. Both wind and pumped storage plant

supply the power to the market at the given market price. PSP is connected with the grid so that it can draw the power from the grid for pumping at given market price whereas pumping using wind power is at constant given price. Grid based pumping energy is limited to 400 MWh per day with a maximum power capacity limit of 100 MW as shown in Table III. Table IV shows the change in the profit of Wind-PSP against the penalty paid as times the market price. Here, profit is the difference between market total revenues and the revenue loss due to market imbalance. Both of the case studies have been solved by using the KNITRO solver under AMPL.

After analyzing these both case studies, it has been seen that PSP units are scheduled to generate power especially in periods with high market price, this help to increase the revenue across the PSP. As shown in Fig. 1 and Fig. 2, between the 4th -7th and 15th to 19th hour, adjustable speed type unit is more successful to reduce the imbalance between the generation and demand to avoid the penalty during high market price. Table 3 shows the profit of Wind-PSP system for both case studies. Profit is taken as the difference between market total revenues and the revenue loss due to market imbalance. For efficient utilization of its output, the pumping is done only when the market price is low otherwise PSP will operate in generating mode as shown in Fig 3 and 4. From these figures it has been seen that during the time period 7th-15th hour and 18th -24th hour market price is high. During this period PSP turbine was operating in generating mode and tried to reduce the market imbalances, whereas between 1st to 7th and 15th-19h hour. it was operating in pumping mode to store the energy in the reservoir to utilize this energy for further power generation.

TABLE I

Pumped Storage Plant Data

Mode of Operation

Efficiency

%

Power Generation and Consumption (in MW)

Conventional unit

Adjustable speed type unit

Max

Min

Max

Min

Gen

84.4

59.65

0

59.65

0

Pump

90.0

76.06

76.06

76.06

46.00

TABLE II

Reservoir Data

Reservoir

Type

Reservoir Capacity (in MWh)

Maximum

Minimum

Initial

Final

Offline

1200

300

600

600

TABLE III

Grid Pumping Data

Power Supplied by Grid for Pumping

Maximum

Minimum

Total

100 MW

0 MW

400 MWh

TABLE IV

Result of wind and pumped storage plant operation

Penalty Factor

Profit

(in thousand Rs)

Revenue Loss

(in thousand Rs)

Case Study 1

Case Study 2

Case Study 1

Case Study 2

0.50

1346.418

1350.639

12.12

3.45

0.75

1340.354

1348.915

18.19

5.17

1.00

1334.291

1347.192

24.25

6.89

1.25

1328.227

1345.468

30.32

8.61

Fig. 1 Wind-PSP Operation for case study 1 (at 0.75 penalty factor)

Fig. 2 Wind-PSP Operation for case study 2 (at 0.75 penalty factor)

Conclusion

This paper presented the operation of Wind-Pumped storage plant (PSP) in Grid connected day ahead market where pumped storage plant operates in either generating or pumping mode and it has been tried to reduce the market imbalance between demand and generation. The objective function is the maximization of the profit, defined as the difference between market revenues and the revenue loss due to market imbalance. Two case studies have been presented and these cases were efficiently solved by KNITRO solver using MINLP technique. The results demonstrate that the used of adjustable speed type PSP improved the reliability of this approach along with increase in the market profit. The proposed approach can be further improved by increase in the number of PSP units.

Fig. 3 PSP Operation for case study 1 (at 0.75 penalty factor)

Fig. 4 PSP Operation for case study 2 (at 0.75 penalty factor)