Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 723127, 8 pages

http://dx.doi.org/10.1155/2015/723127

## An Optimization Scheduling Model for Wind Power and Thermal Power with Energy Storage System considering Carbon Emission Trading

School of Economics and Management, North China Electric Power University, Beijing 102206, China

Received 1 September 2015; Revised 19 October 2015; Accepted 29 October 2015

Academic Editor: Xiaosong Hu

Copyright © 2015 Huan-huan Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Wind power has the characteristics of randomness and intermittence, which influences power system safety and stable operation. To alleviate the effect of wind power grid connection and improve power system’s wind power consumptive capability, this paper took emission trading and energy storage system into consideration and built an optimization model for thermal-wind power system and energy storage systems collaborative scheduling. A simulation based on 10 thermal units and wind farms with 2800 MW installed capacity verified the correctness of the models put forward by this paper. According to the simulation results, the introduction of carbon emission trading can improve wind power consumptive capability and cut down the average coal consumption per unit of power. The introduction of energy storage system can smooth wind power output curve and suppress power fluctuations. The optimization effects achieve the best when both of carbon emission trading and energy storage system work at the same time.

#### 1. Introduction

Carbon emission trading can promote large-scale wind power development and help power industry achieve energy-saving. Wind power output has the characteristics of randomness and intermittence, which puts impact on power system safety and stable operation and makes consumptive problem become the major factor that hinders large-scale wind power development. Power charging and discharging function of energy storage system can smooth wind power output curve, restrain power fluctuation, and provide backup services for wind power grid integration. Therefore, analysis optimization model for thermal-wind power system and energy storage system collaboration scheduling considering carbon emission trading has important sense in improving power system’s wind power consumptive capability.

Literature [1] regarded carbon emission as virtual network flow that attached to the power flow. Based on the analysis results of carbon emission trading and power industry developing trend, a theoretical framework for power system carbon emission was built. Literature [2–4] studied carbon emission right definition problems in cross-regional power trading. An emission right allocation principle was obtained according to the carbon flow tracking mathematical model put forward by those literatures. Literature [5–8] discussed the effects of carbon emission trading. While meeting load demand, CO_{2} emission can be effectively controlled when carbon trading and energy storage systems are both considered.

Wind power output is random and intermittent, which makes its output hard to be accurately predicted [9]. This factor makes wind power consumptive problem hard to be solved. The most effective solution is to control wind power output characteristics [10, 11]. Wind-thermal power system and energy storage system collaborative scheduling provides an effective way to solve this problem [12–14]. Literature [15, 16] put forward an operation model for multiple-time-scale hybrid system collaborative scheduling, which can arrange wind power and energy storage online and provide the specific scheduling information for system operators. Literature [17, 18] studied specific energy storage measures and built a planning model for hybrid system joint scheduling model that combined wind power and pumped storage.

The rest of this paper is structured as follows. Section 2 introduces the optimization models of wind-thermal system in different scenarios, including the basic optimization model, the model considering carbon emission trading, the model considering energy storage system, and the model considering both of carbon emission trading and energy storage system. To verify the correctness of the models put forward by this paper and analyze the influence of carbon emission trading and energy storage system on power system’s wind power consumptive capability, Section 3 demonstrates a numerical example analysis based on 10 thermal power units and wind farms with 2800 MW installed capacity. Section 4 concludes this paper.

#### 2. Optimization for Wind-Thermal System in Different Conditions

##### 2.1. Optimization Model for Wind-Thermal System Collaborative Scheduling

Wind-thermal system optimization collaborative scheduling is aimed at improving wind power consumptive capability. However, wind power grid connection needs thermal power providing backup service to meet demand load. Therefore, overemphasizing the improvement of wind power consumptive capacity would require higher backup service level, which makes related thermal units start up and shut down more frequently and brings more coal consumption and pollutant emission. To improve wind power consumptive capacity and control thermal units’ startup and shutdown, this paper builds a scheduling optimization model of wind power and thermal power. Maximizing the total profit is the optimization objective as follows:wherein is the total profit of wind farms; is the total profit of thermal power units. and could be, respectively, calculated bywherein is the benchmark price of thermal power in power output area; is the real-time output of thermal unit at time ; is power consumption rate of thermal unit ; is fuel cost; is maintenance cost of thermal unit ; is depreciation cost of thermal unit .

Fuel cost mainly consists of coal cost and oil cost as follows:wherein is the procurement price of standard coal; is the real-time output of thermal unit at time ; is standard coal consumption of thermal unit with real-time output ; is an operation or stop status variable of thermal unit at time , if the unit stop and coal consumption is 0; else and coal consumption could be calculated by the consumption characteristic function and real-time generation output . The consumption characteristic function iswherein , , and are parameters of coal consumption function and all greater than 0; is startup cost of thermal power unit at time , if and only if and , and does not equal zero; is the cost of a single startup of thermal unit , including coal and oil costs; is shutdown cost of thermal unit at time , if and only if and , and does not equal zero; is the cost of a single shutdown of thermal unit , including coal and oil costs.

The constraints mainly consist of three aspects, namely, demand side, wind power, and thermal output constraints.

*(**1) Equilibrium Constraint of Power Supply and Demand.* Considerwherein is the demand load at time ; is the line losses rate of power system.

*(**2) Backup Service Constraints.* When power system operates, generation side may be inconsistent with demand side. To ensure real-time equilibrium between supply and demand, thermal units should adjust their outputs to coordinate wind power output to meet load demand. The adjustments should meet some constraints, which are depending on thermal units’ characteristics:

Equations (6) are upper spinning reserve constraints, wherein is the maximum possible output of unit at time ; is upper spinning reserve demand, depending on thermal and wind power output in corresponding periods; is the maximum possible output of unit in unit period, which is determined by installed capacity; is the upper limit of power climbing speed, namely, the biggest power increment of unit in unit period; is thermal power units’ power reserve coefficient; is power reserve coefficient of wind turbine. Consider

Equations (7) are lower spinning reserve constraints. is the minimum output of unit at time , which is determined by two factors: one is the minimum output of unit at the starting state and the other is output-decreasing constraint of unit in unit period; is the lower spinning reserve demand, depending on wind power output in corresponding period; is the minimum output of unit at the starting state in unit time, which is the same as the minimum real-time power output; is output-decreasing speed of unit , namely, the maximum output decrement in unit time.

*(**3) Thermal Unit Real-Time Output Power Constraint.* Real-time output of a thermal power unit is limited by its installed capacity and minimum power output as follows:

*(**4) Output Climbing Speed Constraints.* Influenced by technical level, thermal power output changes in a unit period are limited. Real-time output power increment and decrement should meet

*(**5) Unit Startup and Shutdown Time Constraints.* Frequently startup and shutdown are harmful to unit’s performance and cause more fuel cost. Therefore, constraints for the continuous startup and shutdown time are necessary, as shown in the following equations:

Equation (10) is the minimum startup time constraint; is continuous running time of unit at time ; is the minimum continuous running time. Equation (11) is the minimum downtime constraint; is continuous downtime of unit at moment ; is the minimum continuous downtime.

*(**6) Wind Power Output Constraint.* Wind turbine real-time power output is determined by income air velocity:wherein is the equivalent efficiency of wind farms at time ; is the total installed capacity of wind farms.

##### 2.2. Optimization Model for Wind-Thermal System with Carbon Emission Trading

The introduction of carbon emission trading would redefine thermal power marginal cost, which consists of power generation cost and carbon emission cost. Pollutant emission coefficients of different units are not the same. Therefore, the introduction of carbon emission trading would change the original scheduling plan. To maximize system profit under carbon trading mechanism, this paper built an optimization model with the objective of maximizing the total profit of thermal power and wind power as follows:

The profit of thermal powercan be calculated bywherein is the benchmark price of thermal power in power output area; is self-power-consumption rate of thermal unit ; is the maintenance cost of thermal unit ; is the depreciation cost of thermal power unit .

Carbon emission trading mechanism uses emission cost to measure the environmental value of power generation plans. Without carbon emission trading, the variable cost of thermal units mainly consists of coal cost, oil cost, and water cost. But while carbon emission trading is considered, the thermal unit must buy CO_{2} emission right when its emission exceeds the initial allocated quota level. Therefore, the variable cost of thermal power could be calculated bywherein is the fuel cost that includes coal cost and oil cost; is carbon emission cost, which could be calculated by wherein is actual carbon emission amount of thermal power; is the initial allocated carbon emission right, namely, the allowed CO_{2} emission amount; is carbon emission trading price, determined by the supply and demand relationship in the carbon emission trading market. To simplify the optimization model, this paper hypothesized the price to be a constant value in a short period.

Thermal units’ carbon emission amount is related to its power load rate. Generally speaking, carbon emission of unit electricity production can be integrated as a quadratic function as follows:wherein , , and are parameters of the carbon emission function.

Total carbon emission of the system can be calculated by

Other constraints are the same as the basic model in Section 1, from (6) to (12).

##### 2.3. Optimization Model for Wind-Thermal System with Energy Storage System

While energy storage system is considered, the stakeholders would change from two to three parties. To maximize the total profit, the objective should be changed into (23). Consider wherein is the profit of energy storage system, determined by charge-discharge price, charge-discharge electric quantity, and fixed cost. Consider wherein is energy storage system’s charging power at time ; is energy storage system’s discharging power at time ; is the fixed cost of energy storage system; and are, respectively, charging and discharging price.

Energy storage system can control power charging and discharging, which make it have the characteristics of both power and load. Wind power output opposite distributed with demand load. In daytime, wind power is not sufficient to satisfy demand load and the energy storage system would act as power to meet the demand load. In night wind power output is far exceeding demand load and energy storage system would act as load to transform the extra wind power into potential energy.

The charge and discharge process of energy storage system is determined by real-time load equilibrium and the charging-discharging capability of the energy storage system. Assuming the power that energy storage stored in system at time is , charge-discharge power balance should meet (21). Consider wherein is discharging power at time ; is charge-discharge power loss coefficient that is reflecting the power loss during power transforming.

Charge-discharge capability in unit time is limited by technical level of the energy storage system, as shown in (22) and (23). Consider wherein is the upper limit of energy storage system charge-discharge power in unit time.

Energy storage system power storage capability also has its upper limit.

Considerwherein is the maximum storage capacity of storage system.

For the entire study period, the charged power should be equal to the discharged power as follows:

Based on (25), to ensure energy storage system positive profit, charge and discharge price should meet

At any moment power output should equal demand load as follows:

Other constraints are the same as the basic model in Section 1, namely, from (6) to (12).

##### 2.4. Optimization Model for Wind-Thermal System with Carbon Emission Trading and Energy Storage System

The same with Section 3, in this optimization model the optimization objective is still consisting of three parts as follows: wherein thermal power unit profit is influenced by coal consumption, coal price, carbon emission, and carbon emission price. could be calculated bywherein carbon emission cost is determined by the initial allocated carbon emission right and carbon emission price.

Wind power and thermal power real-time output, energy storage system charge-discharge power, and system load should comply with

Other constraints are the same as the basic model in Section 1, from (6) to (12).

#### 3. Numerical Example Analysis

##### 3.1. Basic Data

This paper did a simulation based on 10 thermal power units and wind power farms with 2800 MW installed capacity. Thermal power units’ operating parameters are referred to in literature [19]. A typical day’s system load and wind load output data is shown in Table 1. Assume wind power tariff to be 540 Yuan/MW·h, maintenance and depreciation costs to be 600 million, and thermal power tariff to be 380 Yuan/MW·h, equivalent to 800 Yuan/t of standard coal price.