## Price Based Unit Commitment Considering Fuzzy Uncertainty

**Reza Khorramnia**^{1,}, **Soroush Karimi Khorrami**^{1}

^{1}Department of Electrical Engineering, Safashahr Branch, Islamic Azad University, Safashahr, Iran

2. Price Based Unit Commitment without Considering Uncertainty

3. Price Based Unit Commitment Considering Fuzzy Uncertainty

### Abstract

In deregulated systems, bidding plays an important role for Gencos participating with the objective of maximizing proﬁt. While making bidding strategies, factors like unit constraint and price uncertainty need to be considered as they have direct impact on the expected proﬁt. The goal of the partnership units of solution is based on the price. By solving this problem, the generation company to determine the optimal generation schedule and unit status hourly. MCP plays an important role in the profitability of the units. In this paper, a novel approach to solving an optimal bid curve underprice uncertainty using PBUC in PAB markets is presented. Numerical results show the suitability of the method on a sample market.

### At a glance: Figures

**Keywords:** price based unit commitment, market clearing price, fuzzy uncertainty, pay as bid, Generation Company

*American Journal of Electrical and Electronic Engineering*, 2013 1 (1),
pp 10-14.

DOI: 10.12691/ajeee-1-1-2

Received December 30, 2012; Revised January 26, 2013; Accepted February 26, 2013

**Copyright**© 2013 Science and Education Publishing. All Rights Reserved.

### Cite this article:

- Khorramnia, Reza, and Soroush Karimi Khorrami. "Price Based Unit Commitment Considering Fuzzy Uncertainty."
*American Journal of Electrical and Electronic Engineering*1.1 (2013): 10-14.

- Khorramnia, R. , & Khorrami, S. K. (2013). Price Based Unit Commitment Considering Fuzzy Uncertainty.
*American Journal of Electrical and Electronic Engineering*,*1*(1), 10-14.

- Khorramnia, Reza, and Soroush Karimi Khorrami. "Price Based Unit Commitment Considering Fuzzy Uncertainty."
*American Journal of Electrical and Electronic Engineering*1, no. 1 (2013): 10-14.

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### 1. Introduction

Unit commitment (UC) in electric power systems is to optimize generating resources to supply system load while satisfying prevailing constraints, such as minimum on/off time, ramping up/down, minimum/maximum generating capacity and fuel and emission limit ^{[1, 2]}. In day-ahead electricity markets, generation companies offer their desirable hourly bid curves to participate in the market of the next day. Because of the significant impact of bid curve on the profit of each generation unit, proposed schedule of unit is very important.

A Genco is a self-interested entity which is responsible for its own risk-based maintenance outage scheduling. Such planned outage schedules will be submitted to the independent system operator (ISO) for approval. A Gencointends to minimize potential ﬁnancial risks when planning its generator maintenance outage schedules ^{[2]}. It is very crucial for a Gencoto devise a maintenance outage schedule which guarantees its potential payoffs. The main factor determining the unit is turned off or on, is the MCP that ISO determine it.

As the market requires Gencos to bid for each unit separately or in the market with insignificant market power, the UC for each generating unit can be considered independently. Hence, for profit maximizing objective, it is profitable to operate a unit as long as the cost of producing is lower than the revenue obtained by selling that quantity produced ^{[2]}.

Arroyo and Conejo ^{[3]} proposes a 0/1 mixed integer linearprogramming to maximize the unit profit from selling bothenergy and spinning reserve in spot market. Leou and Y. N. ^{[4]} Chang proposes a PUBC^{3} problem considering uncertainties of energy price at the stance of GENCOs. This problem is solved by the greedy algorithm and quadratic program using the concept of decommitment. A selective enumeration technique has been proposed in ^{[5]} to solve the PBUC problem using heuristic technique in coordination with dynamic programming and non-linear programming.

Ref ^{[6]} solve the problem for thermal and combined cycle units with pump storage solution and compare it with LR method. Finally It is expressed proposed method is beter.

All the proposed methods are, however, based on cost minimization objective, similar to the one used for the traditional markets. But, in deregulated markets, Gencos are usually entities owning generation resources and participating in the market with sole objective of maximizing the profits without concern of the system unless there is an incentive for it. Hence, if we consider generation planning for a period of, say 24 hours in advance, the Gencos based on the price forecast, generation unit characteristics, unit availability etc carryout profit based unit commitment (PBUC) and thereby determine the bidding strategy for each bidding period next day. In real time, they would have to meet generation as ordered by the ISO ^{[7]}.

In this article, price uncertainty is considerd and supposeit has a fuzzy membership function. Also,It is assumed that the model of power market is PAB^{4} Numerical examples is presented the effectiveness of the proposed method.

### 2. Price Based Unit Commitment without Considering Uncertainty

Primitive and definitive solution to simplify the problem by assuming that market price is certain.

In most power markets, a company must be produced for each unit independently owned their proposed schedule to provide that in this case, the problem of PBUC for each unit is solved independently ^{[5]}.

**2.1. Description of Problem**

Since the schedule of Genco is determined by ISO, problem significance especially in terms of price uncertainty is clearer. The goal of the price-based unit commitment is to maximize the profit (i.e., revenue minus cost) of GENCOs subject to all constraints. This new price-based UC problem is different from traditional cost-minimization UC.

**2.2. Problem Formulation**

In the deregulated environment, market prices are unknown when GENCOs propose their bids. Therefore, this new algorithm should consider uncertainties exiting in price and the objective function is to maximize. Besides, the new UC problem doesn't consider satisfying load demand as its necessary constraint. The objective function and constraints of this model are described below. The objective function of this model is first depicted as follow:

(1) |

(2) |

### 3. Price Based Unit Commitment Considering Fuzzy Uncertainty

**Fig**

**ure**

**1.**Unit benefit function and cost function

In actual power markets, due to the multiplicity of different Gencos and the multiplicity of bids, MCP of the market is an uncertain variable.

Unit Profit function from sales of energy and unit cost function is shown in the Figure 1. As can be seen, profit equals the difference between revenue and cost and greatest benefit may not occur in most generation.

**3.1. Modeling Uncertainty with Fuzzy Price**

The MCP is modeled as both, probability models ^{[4, 8, 9]} and the possibility ^{[10, 11]}. In this paper, we use possibility model and price uncertainty is modeled as fuzzy variables and membership function for MCP uncertainty is shown as in Figure 2.

**Fig**

**ure**

**2.**Fuzzy membership function of MCP

Figure 3 shows a membership function of possibility of price acceptance.

**Fig**

**ure**

**3.**Fuzzy membership function of Acceptance price

We can assume that the set P is the set of all possible price cuts of alpha (α - Cut) and fuzzy set market prices settle in relationships can be defined:

(3) |

(4) |

**3.2. Formulating the Problem**

Profits and optimum production have a sensitive relation with price. And other hands, the optimal operating point will be different for different prices .Price predictions have always been a period of change and uncertainty is therefore better results can be obtained by fuzzy model, as the price of uncertainty.

(5) |

: fuzzy Price prediction for hour(t)

(6) |

**3.3. Constraints of Problem**

**3.3.1 Minimum/Maximum Generation**

(7) |

P_{min}: Generation Lower Limit of Unit

P(t): Generation of Unit *i for hour (t)*

P_{max}: Generation Upper Limit of Unit

**3.3.2 Up/Down Rate of Generation**

(8) |

(9) |

DR: Down Rate of Generation

UR: Up Rate of Generation

**3.3.2 Minimum Up/Down Time of Unit**

(10) |

(11) |

**3.4. Profit Calculated as a Fuzzy**

Given that the price variable is a fuzzy model, fuzzy variables in the form of Figure 4 will be. Sometimes, may be the unit status is changed (on or off) for different values of the fuzzy membership function. The dependence of the unit generation at different times to each other, and the constraints on the problem, lead to the generation scheduling is difficult with solving the problem by proposed method for alpha -cutting , profit and production planning will be different. benefits of each section related to alpha [13] can be expressed:

(12) |

(13) |

Optimal schedule of generation is calculated by equation [15]. In this regard, the combination of benefit and risk is optimized and acceptable risk level to the possible degree (n), is modeled. Parameter value of "n" in the examples and experience on the matter shall be determined by an expert.

(14) |

(15) |

**Fig**

**ure**

**4.**Fuzzy membership function of profit

### 4. Numerical Example

**Fig**

**ure**

**5.**Fuzzy membership function of MCP for Sample hour

**4.1. Impact of Price Uncertainty**

In this section we shall assume that the market price is certain. Since the purpose of comparison between the results of different methods, is price uncertainty, it is assumed that the values chosen for the certain MCP, is A3, corresponding point of fuzzy membership function. This price is the highest possible (with membership value equal to 1) to have comparable results.

**4.2. Considering Uncertainty in the Fuzzy Price**

**Fig**

**ure**

**6.**Fuzzy membership function of profit

**Fig**

**ure**

**7.**Fuzzy membership function of MCP and profit

In this numerical example, the effect of price uncertainty is represented in the final results, it is clear that the uncertainty can improve the unit profit. The hours that the unit is off, turn on/off cost (20$),lead to negative profit at this time.

**Fig**

**ure**

**8.**Fuzzy sets (A9, 0. 5) for fuzzy variable profits and MCP

The hours that the unit is off or on, leads to negative profits. It is possible for the generation benefit is positive, but due to the high unit cost, total profit is negative.

With respect to the previous section, in the optimum production schedule, the profit and risk of accepting is appropriate.

### Conclusion

This paper proposed a novelapproach of unit scheduling under price uncertainty using PBUC. The proﬁt obtained using PBUC considering price (MCP) uncertainty is the membership function of Trapezoidal function. Use alpha-cut method to defuzzification final profit.

The method is tested with a numerical example to analyse the effect of the price uncertainty on the expected proﬁt. Comparisons made show that the proposed method results in higher expected proﬁts under price uncertainty. Hence, for decision makers, this method can be a tool for improving the expected proﬁts.

### References

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[3] | J. M. Arroyo and A. J. Conejo, “Optimal response of a thermal unit toan electricity spot market,” IEEE Trans. Power Syst., 15(3): 1098-1104, 2000. | ||

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[9] | G. B. Shrestha, B. K. Pokharel, T.T. Lie, and S. E. Fleten, “Price-based unit commitment for bidding under price uncertainty”, IET Gener. Transm. Distrib., 1 (4): 663-669, 2007. | ||

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[10] | P. Attaviriyanupap, H. Kita, E. Tanaka and J. Hasegawa, “A Fuzzy-Optimization Approach to Dynamic Economic Dispatch Considering Uncertainties,” IEEE Trans. Power Syst., 19(3): 1299-1307, 2004. | ||

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### Notes

^{1}^{2}- Generation Company^{3}- Market Clearing Price^{4}- Lagrangian Relaxation