Mathematical Problems in Engineering

Volume 2016 (2016), Article ID 4070251, 10 pages

http://dx.doi.org/10.1155/2016/4070251

## A Joint Scheduling Optimization Model for Wind Power and Energy Storage Systems considering Carbon Emissions Trading and Demand Response

^{1}School of Economics and Management, Beijing University of Aeronautics and Astronautics, Beijing 100191, China^{2}School of Economics and Management, North China Electric Power University, Beijing 102206, China

Received 16 November 2015; Revised 11 January 2016; Accepted 27 January 2016

Academic Editor: Jinyun Yuan

Copyright © 2016 Yin Aiwei 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

To reduce the influence of wind power random on system operation, energy storage systems (ESSs) and demand response (DR) are introduced to the traditional scheduling model of wind power and thermal power with carbon emission trading (CET). Firstly, a joint optimization scheduling model for wind power, thermal power, and ESSs is constructed. Secondly, DR and CET are integrated into the joint scheduling model. Finally, 10 thermal power units, a wind farm with 2800 MW of installed capacity, and MW ESSs are taken as the simulation system for verifying the proposed models. The results show backup service for integrating wind power into the grid is provided by ESSs based on their charge-discharge characteristics. However, system profit reduces due to ESSs’ high cost. Demand responses smooth the load curve, increase profit from power generation, and expand the wind power integration space. After introducing CET, the generation cost of thermal power units and the generation of wind power are both increased; however, the positive effect of DR on the system profit is also weakened. The simulation results reach the optimum when both DR and CET are introduced.

#### 1. Introduction

The implementation of China’s energy-saving and pollutant emission reduction strategies has prompted large-scale wind power development. In 2014, the installed capacity of wind power reached 115 million kW, ranking first in the world. However, influenced by the intermittency that is characteristic of wind power, the growth rate of wind power grid integration is smaller than the growth rate of the installed capacity. This phenomenon leads to a high rate of curtailed wind power in China. The average rate of curtailed wind power is approximately 12.8%. Especially in the “three north areas,” the rate of curtailed wind power has already reached 15.4%. In order to solve the problem of curtailed wind power, suitable backup service should be provided on the generation site for wind power connected to the grid. Energy storage systems (ESSs) could flexibly provide backup service by charging and discharging. This property gives ESSs the most potential as a means to provide backup service for wind power integration. Additionally, demand response (DR) could optimize customers’ power consumption behavior and incentivize customers to participate in system scheduling for wind power consumption.

Currently, China is implementing carbon emission trading (CET) pilot projects and plans to establish a CET market to prompt energy-saving and emissions reduction in the “thirteenth five-year plan” period. CET could affect the generation cost of thermal power units and make clean energy generation more advantageous. Hetzer et al. [1] regard carbon emission as a virtual network flow to subsequently build a theoretical framework for carbon emissions from the power system based on analyses of carbon emission trading and developing trends in the power industry. References [2–4] study carbon emission right definition problems in cross-regional power trading and build a fair allocation principle based on the construction of a mathematical model that tracks carbon flow. The above research shows that CET can affect the cost of thermal power generation and make grid integration of clean energy more advantageous. Therefore, a study of how to integrate ESSs, DR, and CET into the traditional generation scheduling of a power system with wind power has important practical significance.

Selecting a better backup method is the most effective way to overcome the random nature of wind power. Currently, backup service for wind power grid integration consists of three main parts: thermal power, pumped storage power plants, and ESSs. Jiang et al. [5] develop a wind-thermal economic emission scheduling model considering coordination of the power allocation of thermal units and wind turbines. Yuan et al. [6] establish a multiobjective economic scheduling model for the hydrothermal-wind problem, considering the uncertainty cost of wind power. Wang et al. [7] propose a novel stochastic constraint model to solve for the uncertainty cost of wind power and present an improved particle swarm optimization (PSO) algorithm to solve the proposed model. Thermal power units can provide backup service for wind power by adjusting their start-stop condition, but their fuel consumption and pollution emission are not environmentally friendly. Therefore, pumped storage power stations are a better way to provide backup service. Papaefthymiou et al. [8] achieve high penetration levels of renewable energy in power systems by combining wind power and pumped storage power plants. Papaefthymiou and Papathanassiou [9] propose a novel unit commitment problem model and binary PSO algorithm to find the optimal schedule scheme. Ming et al. [10] calculate the effect of pumped storage power stations on wind power regulation and develop an economic evaluation model for combined wind power and pumped storage systems. Pumped storage power plants have the advantages of saving energy and reducing pollutant emission, but they are not suitable for large-scale application because they are restricted by geographic location and conditions.

The operational theory of ESSs is similar to that of pumped storage power plants, but ESSs have more flexible installation requirements with better prospects for large-scale application. Wu et al. [11] take constraints on power generation units and energy storage units into consideration and build a static model for joint operation of wind power and energy storage. Hu et al. [12] combine opportunity and constraint theory and build a joint scheduling model for wind power and energy storage systems considering the uncertainty in wind power output, which is applied with good results. Ding et al. [13] build a wind-storage joint scheduling model considering risk constraints and use a Monte Carlo simulation method to simulate wind power output. García-González et al. [14] improve the power ramp mathematic expression for wind power and build a joint scheduling optimization model for the control of curtailed wind power and energy storage systems.

The researchers cited above have achieved good results in actual applications; however, the high initial investment cost limits the scale of application of energy storage systems. Therefore, other routes are needed to optimize the application of ESSs. DR can optimize customers’ power consumption behavior, smooth the demand load curve, and increase the consumption of wind power. Greening [15] puts forward the basic concept of demand response. Niu et al. [16] classify DR into price-based demand response (PBDR) and incentive-based demand response (IBDR). López et al. [17] propose an optimization model for performing load shifting in the context of a smart grid. Nwulu and Xia [18] integrate game theory into dynamic economic emission scheduling considering DR. A framework for optimizing the bidding strategy of a smart distribution company that contains wind farms and responsive loads in the day-ahead energy market is proposed by Ghasemi et al. [19]. Wang et al. [20] construct a modeling framework for an integrated electricity system in which loads become an additional resource.

CET can highlight the environmental friendliness of wind power and increase the advantages of wind power generation [21]. Zhu et al. [22] developed a full-infinite fuzzy stochastic programming method for planning municipal electric power systems associated with greenhouse gas control under uncertainty. Khalid and Savkin [23] developed and tested a methodology for controlling the emissions from a group of microgenerators aggregated in a virtual power plant with wind power. The above papers discussed the impact of CET on system scheduling; the effects of collaborative optimization of CET, ESSs, and DR should be analyzed.

The rest of this paper is organized as follows. Section 2 puts forward a demand response mathematical model. Section 3 presents a model for charging and discharging ESSs. Section 4 establishes the joint scheduling optimization model for wind power and ESSs with and without CET. Section 5 takes 10 thermal units, a wind farm with 2800 MW of installed capacity, and 3 × 80 MW ESSs as the simulation system and comparatively analyzes the influence of ESSs, DR, and CET on system operation. Section 6 presents the primary conclusions.

#### 2. Demand Response Model

Power demand response refers to a situation in which customers dynamically adjust their power consumption behavior according to price, which should guarantee a balance between power supply and demand. From an economic point of view, when electricity price increases, the demand for power should decrease. Part of the power demand during the peak load period will be transferred to other periods, while the other part will be reduced. Thus, for the peak load period, the load reduction consists of three parts: one is load transfer due to an increased electricity price, the second is load reduction, and the third is load transfer due to a reduced electricity price during the valley load period. For the float load period, the load change consists of two parts: one part comes from the peak load period and the other part goes to the valley load period. For the valley load period, the load increase consists of three parts: one is load transfer due to a decreased electricity price, the second part comes from the peak load period, and the third part is new power demand due to the price reduction.

This study defines the power demand during the peak load period, float load period, and valley load period before implementing time-of-use (TOU) price as , , and . Power demand at period is ; therefore,

The proportion of power demand reduction during the peak load period is given by , the proportion of the load that transfers to other periods is and the load loss proportion is , and the proportion of the load that transfers to the float load period is and the proportion that transfers to the valley load period is . The proportion of power demand increase during the valley load period is , the proportion of the load transferred to the valley load period is , and the new demand proportion is . The proportion of the load that comes from the valley load period is , and the proportion from the float load period is . Thus, the demand during the peak, float, and valley load periods is calculated as follows:

If the proportion of load change is the same at each point in time in the same period, the load at each time point is

The system load period will change from to with the introduction of DR; load demand reduces during the peak load period and increases during the valley load period. The demand load curve becomes smoother after peak load shifting.

#### 3. Charging and Discharging Model for ESSs

ESSs can be regarded as both power resources and load demand. When wind power output is high at night, ESSs are regarded as load demand. In the daytime, they are regarded as power resources to meet load demand. Charge and discharge of ESSs are limited by the system capacity. Assuming the storage energy of ESSs at time is , the charging and discharging power balance should obeywhere is the charging power at time , is the discharging power at time , and is the loss coefficient for charging and discharging power.

Charging and discharging power from ESSs is limited as follows:where is the upper limit for charging and discharging power.

In addition, the energy storage capacity of ESSs is limited: where is the maximum storage capacity of the ESSs.

#### 4. Scheduling Model for Wind Power and ESSs

##### 4.1. Mathematical Model without CET

###### 4.1.1. Objective Function

Wind farm operators hope for higher consumption of wind power to gain more profits; however, this will cause more frequent adjustment of thermal power units for peak regulation, improving wind power grid integration but also increasing system coal consumption. To achieve the optimum energy efficiency, a joint optimization scheduling model for wind power and thermal power is built. The maximum total profit of ESSs, wind power, and thermal power is taken as the optimization objective:where , , and are the profits of wind farms, thermal power units, and ESSs, respectively.

The wind farm profit is calculated as follows:

The profit of thermal power units is calculated as follows:where is the benchmark price of thermal power, is the real-time power generation of unit at time , is the power consumption rate of unit , is the fuel cost for power generation, is the operation and maintenance cost of unit , and is the depreciation cost of unit .

The fuel cost of a thermal power unit is calculated bywhere is the standard coal purchase price, is the standard coal consumption, and is a binary variable. When a thermal power unit is shut down, coal consumption is zero, when the thermal power unit is operating, coal consumption is determined by the consumption characteristics function and the real-time power output :where , , and are coal consumption parameters of unit , is the start-up cost of unit at time , is the start-up cost of unit , is the shutdown cost of unit at time , and is the shutdown cost of unit :where is the electricity price when charging ESSs, is the electricity price when discharging, and is the fixed cost of the ESSs.

###### 4.1.2. Constraint Conditions

In the joint optimization model, the constraints of demand and supply balance, thermal power unit operation, wind power operation, and ESS operation should be comprehensively considered.

*(1) System Demand and Supply Balance Constraint*. Before DR, the system demand and supply balance constraint is described by

After DR, the constraint is described by

*(2) Thermal Power Unit Power Generation Constraint*. Real-time generation output is limited by the installed capacity and the minimum generation output:

*(3) Unit Ramp Rate Constraint*. Depending on the technology level, unit generation output change is constrained by the adjacent period. The real-time output increment and decrement should obey

*(4) Unit Start-Stop Time Constraints*. Frequent start-stop affects the performance of a thermal unit. The continuous unit start-stop constraint is shown as follows:

Equation (17) is the shortest time constraint on unit . is the continuous running time of unit at time . is the shortest running time of unit . Equation (18) is the shortest shutdown time constraint on unit . is the continuous shutdown time of unit at time . is the unit shortest shutdown time.

*(5) Wind Power Output Constraint*. The real-time wind power output is constrained by the wind farm capacity:where is the equivalent utilization efficiency and is the total installed capacity of wind farm .

*(6) Charging and Discharging Power Constraint on ESSs*. For ESSs, the cumulative charging and discharging power should obey

Therefore, if ESS operators hope to profit, the charging and discharging prices should obey

*(7) System Generation Reserve Constraints*. When the power system is in operation, fluctuations may happen on both the generation side and the demand side. To ensure real-time balance, the supply of power should be adjusted to fall within a certain margin by increasing or reducing the power output:

Equations (22)–(24) are the system upward spinning reserve constraints. is the maximum possible output of unit at time . is the upward spinning reserve demand, depending on thermal and wind generation power in the corresponding period. is the maximum possible energy generation by unit at time , adjusted for the installed capacity. is the upward ramp rate, namely, the maximum power generation in the adjacent period. is the thermal power unit reserve coefficient. is the power reserve coefficient for wind turbines:

Equations (25)–(27) are the system downward spinning reserve constraints. is the minimum possible output of unit at time , restricted by two factors, namely, the minimum possible generation capacity under operation and the unit downward ramp rate constraint. is the system downward spinning reserve demand, depending on wind power in the corresponding period. is the minimum possible generation capacity of unit , adjusted for the real-time minimum power output. is the unit downward ramp rate, that is, the maximum power reduction generation unit in the adjacent period.

##### 4.2. Mathematical Model with CET

Currently, China is performing pilot construction and planning to establish a CET market in the “thirteenth five-year plan” period. CO_{2} emission from the thermal power industry accounts for approximately 40% of the total. Generation rights displacement and the CET mechanism are both market mechanisms to optimize the thermal industry structure and reduce energy consumption and emission, which are consistent in purpose and results.

The marginal generation cost of thermal power changes under a CET mechanism, and carbon emission parameters are different due to different unit technologies, so the generation scheduling plan also changes. To maximize system profit under a carbon trading mechanism, this study builds an optimization model with the objective of maximizing thermal and wind power profit:

Thermal power profit should meet the following conditions:where is the cost of carbon emission:where is the actual carbon emission of thermal units during the operation period, is the total initial carbon emission right, and is the carbon trading price, which is related to the carbon trading demand. To simplify the model, this study assumes that the price does not change with the carbon trading demand.

The actual carbon emission of thermal units is related to the power load rate. Generally speaking, the actual carbon emission of units can be expressed as a quadratic function, similar to (22):where , , and are parameters of the carbon emission function.

Then, total system emissions are as follows:

Scheduling and operation constraint conditions for wind power and ESSs should be considered comprehensively in carbon emissions trading. The system demand and supply constraints, wind power unit operation constraints, and ESSs operation constraints are shown in (13) to (27).

In the mathematical model without CET, (10), (11), (17), (18), and (31) are nonlinear constraints, which are inconvenient to solve. Therefore, they should be linearized. The details of this process can be found in the literature [24, 25].

#### 5. Example Analysis

##### 5.1. Case Descriptions

To analyze the impact of ESSs, DR, and CET on system operation, four cases are set up as follows.

*Case 1 (baseline case). *
Self-scheduling of the system without DR and CET: DR and CET are not considered, so the impact of ESSs on wind power grid integration is analyzed alone in this case. The ESS capacity is 3 × 80 MW, the charging and discharging power of a single ESS unit is 20 MW, and the charging and discharging loss coefficient is 15%.

*Case 2 (self-scheduling of the system with DR). *Demand response is introduced into the joint scheduling. The demand load curve is divided into peak, valley, and float load periods according to the literature [24], which are listed in Table 1. The values of and are 0.95 and 0.7, respectively, and are 0.90 and 0.40, respectively, and both and are 5%.