Adjustable robust power dispatch with combined wind-storage system and carbon capture power plants under low-carbon economy

Electrical Power and Energy Systems 113 (2019) 772–781

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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes

Adjustable robust power dispatch with combined wind-storage system and carbon capture power plants under low-carbon economy

T

⁎

Rufeng Zhanga, Tao Jianga, , Linquan Baib, Guoqing Lia, Houhe Chena, Xue Lia, Fangxing Lic a

Department of Electrical Engineering, Northeast Electric Power University, Jilin, JL 132012, China Systems Engineering and Engineering Management, University of North Carolina at Charlotte, Charlotte, NC 28213, USA c Department of Electrical Engineering and Computer Science, The University of Tennessee, Knoxville, TN 37996, USA b

A R T I C LE I N FO

A B S T R A C T

Keywords: Robust power dispatch Low carbon economy Carbon capture power plants Combined wind-storage system

This paper proposes an adjustable robust power dispatch (ARPD) model under low-carbon economy to accommodate the uncertainty of wind power with combined wind-storage system (CWSS) and carbon capture power plants (CCPPs). First, battery energy storage (BES), which is considered as adjustable under worst-case scenarios, is introduced to wind power plants to form a combined wind storage system structure to improve operation flexibility. Then, a dispatching model of CCPPs is presented and analysed. The operating characteristics of CCPPs make it possible to control net power outputs and carbon emissions independently and flexibly. The integration of BES and carbon capture and storage (CCS) improves the operation flexibility of both wind power plants and conventional power plants. The objective function of the proposed model under intervaluncertain wind power is to minimize the total cost under the worst wind power output case and the context of low-carbon economy. The proposed model is implemented on the modified PJM 5-bus system with one wind farm and the IEEE-118 bus system with five wind farms. Numerical results demonstrate that the proposed model is effective at reducing carbon emissions and wind power curtailment, and verify that as the number of CCPPs increases, the overall costs come down.

1. Introduction Global warming caused by CO2 has made it essential to develop low carbon economy [1]. For example, the carbon emissions reduction target scheme of the UK government is to achieve 80% reduction by 2050 compared to the emissions level of 1990 [2]. The power industry is regarded as one of the largest producers of emissions, and carbon emissions should be taken into consideration in the process of power system dispatch to achieve emissions reduction goals [3]. Hence, research on the operation of power systems under low carbon economy is of great significance [3–5]. Promoting renewable energy integration and applying carbon capture and storage (CCS) technology in conventional power plants can contribute to reducing CO2 emissions [6]. CCS technology has been regarded as one of the most promising options to reduce anthropogenic CO2 emissions from fossil fuel fired power plants, which is a major source of CO2 emissions [6,7]. CCS technology incorporated in a fossil fuel fired power plant can capture CO2 and transport it to a storage location with the consumption of a certain amount of energy. The consumed power introduces an “efficiency penalty” effect to the plant,

⁎

resulting in net output reduction [8,9]. Carbon capture power plants (CCPPs) control power output and carbon emissions separately, which provides the operation flexibility [10]. The flexible operation mechanism of CCPPs has been modeled in [8] and [10]. Such operation flexibility has a significant impact on power system economic dispatch under low carbon economy. Economic dispatch with CCPPs has been studied in [10–12], but none of them considers the operation within a renewable energy context. Integration of large-scale volatile wind power can reduce fossil fuels consumption and carbon emissions by replacing part of the conventional power output, but such integration will create challenges for power system operation and dispatch. Such volatility (determined by volatile wind speed) and inflexibility, which may result in wind power curtailment, are some of the disadvantages of wind power. Energy storage (ES) is an effective way to provide technical and economic benefits to power systems, in which battery energy storage (BES) is a valid element in the design of wind power dispatch [13]. An approach for planning and operating in the electricity market from the view of combined wind storage systems (CWSS) is proposed in [14]. Compared to common wind power plants, CWSS can provide more flexible power

Corresponding author. E-mail address: [email protected] (T. Jiang).

https://doi.org/10.1016/j.ijepes.2019.05.079 Received 13 December 2018; Received in revised form 10 April 2019; Accepted 29 May 2019 Available online 15 June 2019 0142-0615/ © 2019 Elsevier Ltd. All rights reserved.

Electrical Power and Energy Systems 113 (2019) 772–781

R. Zhang, et al.

PCG, i, t / PCN, i, t Pi,t PSOCmax PSOCmin Rd Rdown/Rup S0,i,t Sccpp,i,t si,t T U αC αC,max αj,t, βj,t η ηc/ηd ηccpp μl-j,t, πl-j,t

Nomenclature ΔEc/ΔEd charging/discharging rates of BES Aid, t / Aiu, t downward/upward adjusted power (MW) cC cost coefficients of CO2 emissions ($/t) ci bidding prices of conventional unit i ($) cwind bidding prices of wind power units ($) Eccpp,i,t captured CO2 emissions of unit i at period t (t) EG,i,t/E N,i,t gross/net CO2 emissions of unit i at period t (t) EP,i,t amount of CO2 emissions being treated (t) eG emission intensity per unit of gross power output (t.MW) Hi/Gi the ith row of matrices H and G Liml limit for power flow of line l (MW) Ni/Nj number of conventional/wind power units Pw,j,t dispatched wind power (MW) Pc,j,t/Pd,j,t charging /discharging power of jth BES at period t (MW) PCWSS,t dispatching power output of CWSS (MW) PCEP power consumption of CCS (MW) , i, t ,B EP , OP PCEP basic/operation power consumption of CCS (MW) , i, t / PC , i, t Pwf , j, t base-case dispatched wind power output (MW)

gross/net generation output (MW) base output of conventional units (MW) maximum value of SOC (MWh) minimum value of SOC (MWh) reserve requirements (MW) up/down reserve requirements (MW) initial volumes of solvent in the tanks dynamic volumes of solvent in the tanks participation factors number of dispatching periods adjustable uncertainty sets carbon capture rate maximum value of carbon capture rate dual variables auxiliary variable charging/discharging efficiency of BES operating energy penalty rate of CCPPs dual variables

is proposed in this work for the first time. The main motivation of adapting adjustable robust optimization is: for adjustable robust optimization, adjustable variables can be adjusted to make the solutions feasible under uncertain scenarios, and BES considered in this paper is also used to provide adjustable contributions with preset participation factors to maintain power balance under worst-case uncertain scenarios. To analyze the impact of ranging participation factors on the dispatching of BES, adjustable robust power dispatch method is adapted. BES is incorporated in wind farms to reduce wind power curtailment (carbon emissions can also be reduced) and to provide adjustable resources under uncertain scenarios. CCPPs are considered to reduce carbon emissions under low-carbon economy. A low carbon robust dispatch model is formulated to minimize total operation costs, with consideration of carbon emission costs raised by low carbon economy. Operation constraints of BES and CWSS are imposed, and wind power curtailments and carbon emissions can be reduced. Quick regulated conventional units are selected as adjustable units and BES is also used to provide adjustable contributions with preset participation factors to maintain power balance under worst-case uncertain scenarios. Compared with the existing works, the major contribution of this paper can be summarized as follows.

output. Another disadvantage of wind power is uncertainty. Previously, robust optimization has been utilized to address uncertainties in power system operations [15–23], by seeking a solution for immunizing against all possible uncertain scenarios. In [15], a robust scheduling scheme for energy storage systems (ESSs) is presented to facilitate high penetration of renewable energy sources. Bertsimas et al. [16] formulates the security constrained unit commitment (SCUC) problem as a two-stage adaptive robust optimization model and a Benders decomposition type algorithm is employed to solve the model. Robust interval wind power dispatch approaches for look-ahead dispatch are developed in [17,18], in which the decision variables include not only the dispatched wind power, but also the allowable wind power output intervals. Adjustable robust optimization is a type of robust optimization, in which decision variables include here-and-now variables (‘non-adjustable variables’) and wait-and-see variables (‘adjustable variables’) [19]. Adjustable variables can be adjusted to make the solutions feasible under uncertain scenarios. An adjustable robust optimization approach has been successfully utilized for transmission network expansion planning [20], optimal power flow [21,22] and economic dispatch [23]. However, low carbon economy is not considered in the above works. To the authors’ best knowledge, an adjustable robust power dispatch (ARPD) framework from the perspective of low carbon economy

(1) An adjustable robust power dispatch model with CWSS and CCPPs is proposed to account for uncertainties under low-carbon

Conventional units

CWSS

Carbon emission

Wind power generator

Net carbon emission

Power grid Net power output

BES

Operation power consumption

CCS CCPP

Fig. 1. Schematic of the CWSS and CCPPs system. 773

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the power mismatch caused by wind power uncertainties.

economy, in which CO2 emissions costs arisen from the low-carbon policy are considered and the allowable wind power output intervals are also calculated. As compared to robust optimization models in [15–22], the proposed robust dispatch model is carried out under low-carbon economy, and the robust dispatch model is transformed into a single level LP problem, which can be effectively solved with CPLEX. (2) BES and CCS are considered in this paper to improve the operation flexibility of power outputs on the supply side. On the one hand, as compared to the low carbon dispatch models in [3,11,12], based on the charging/discharging capacities of BES, the joint outputs of CWSS in this paper are more flexible than those of wind farms without BES. Moreover, BES is considered to provide regulating capacities under uncertain scenarios to ensure power balance. On the other hand, for conventional power plants with CCS, the power consumption of CCS can be flexibly regulated to adjust the net output of CCPPs. (3) In the proposed robust dispatch model, carbon emissions from power plants are considered as controllable variables to minimize total carbon emissions. The benefits of integration of CWSS and CCPPs are analyzed. The impact of CWSS and CCPPs on carbon emissions and wind power curtailment reduction is quantified and compared. (4) Uncertainty of wind power is represented as forecasting wind power intervals and the allowable wind power generation interval is calculated to provide additional operation information to independent system operators (ISO).

BES obviously cannot be operated to charge and discharge in the same period. The power that a CWSS is dispatched at period t equals to the sum of the dispatched wind power and the charging/discharging power of BES and cannot exceed the forecasting output under base case, which can be expressed as: BES 0 ⩽ PCWSS, t = Pw, j, t - PcBES , j, t + Pd, j, t ⩽ Pw, j, t

(1)

(b) Operation model of CCPPs Post-combustion, pre-combustion and oxy-fuel combustion CCPPs are the three major types of CCPPs, which differ in the integration section between the generation unit and CCS [11]. CCPPs with postcombustion have been utilized in practice and hence are selected in this paper. The structure of benchmark post-combustion based CCPPs are presented in detail in [8]. The existing studies show that post-combustion CCPPs could be operated flexibly to change net output by controlling captured carbon emissions independently. CCS operation is powered by the plant where it is located. However, the power consumption of CCS is not negligible, which will lower the net output of CCPPs. Such a decrease in output would result in reduced operation profits and energy penalties to the plant. The power output of the plant injected into the grid decreases due to the integration of CCS, which is regarded as an efficiency drop in generation. Net generation output PCN, i, t (the electricity delivered to the power grid) equals gross generation output PCG, i, t minus the energy consumed PCEP , i, t by carbon capture systems. The net output is as shown in (2):

2. Flexible operation of CWSS and CCPPs In this paper, CCS and BES are introduced to improve the rate of wind power utilization and reduce carbon emissions. The schematic of the CWSS and CCPPs system is shown in Fig. 1. BES can reduce wind power curtailment directly and carbon emissions indirectly, while CCS can reduce carbon emissions directly and wind power curtailment indirectly. The power outputs of CWSS and CCPPs can be operated flexibly to reduce wind power curtailment, and carbon emissions of CCPPs can be controlled flexibly by capturing various amounts of CO2.

PCN, i, t = PCG, i, t − PCEP , i, t

(2)

In flexible operation mode, the net output of CCPPs can be adjusted by regulating the operation power consumption PCEP , i, t , which is approximately proportional to the carbon capture rate. The power consumption PCEP , i, t of CCS consists of two parts: basic power consumption ,B PCEP , i, t , which is supposed to be constant, and operation power con, OP , OP as shown in (3). PCEP is formulated as (4). sumption PCEP , i, t , i, t

(a) Operation of combined wind-storage system Wind power output is volatile because it is determined by wind speed and the transformation characteristic of wind turbines. Such volatility means that wind power is not completely controllable or dispatchable. In our previous work [24], the structure of a CWSS is presented, consisting of wind generators and BES connected to the same bus in a power system. With the advantage of having flexible charging/ discharging ability, BES is effective at smoothing out fluctuating wind power and making CWSS power output more flexible. BES can also reduce wind power curtailment. In this paper, the further goals of implementing CWSS are:

EP , B EP , OP PCEP , i, t = PC , i, t + PC , i, t

(3)

, OP PCEP = ηccpp × αC × eG × PCG, i, t , i, t

(4)

In this paper, CCS is considered to be operated at full-load or partialload. The net output of CCPPs is related to the operation condition by adjusting αC in the range of 0 – αC,max (80–95%), as shown in (5) and (6):

PCN, i = PCG, i − PCEP , i, t ,B = (1 − ηccpp × αC × eG ) × PCG, i − PCEP , i, t

(1) To provide more flexible and dispatchable power output to the grid, reducing not only wind power curtailment, but also carbon emissions. BES charges/discharges power to reallocate dispatchable wind power across the dispatching time horizon, contributing to peak load regulation. If the BES cannot store some power due to the limitation of the maximum charging capacity or charging rate, such extra power will be discarded (i.e. wind power curtailment). Hence, both wind power curtailment and power output from fossil fuel fired power units can be reduced, which will help to reduce carbon emissions indirectly under low carbon economy. (2) BES can be operated under uncertain scenarios to accommodate wind power uncertainty and ensure power balance within its operation constraints [21]. The charging (or discharging) ability of BES can be treated as a type of adjustable resource responding to

0 ⩽ αC ⩽ αC max

∀ i ∈ GCCPP

(5) (6)

Certain amount of CO2 can be captured and stored by CCS. The operator can adjust the amount of captured CO2 to determine operation , OP power consumption PCEP , i, t . By adjusting the carbon capture rate (the operation power consumption is also adjusted), the CO2 emission intensity of CCPPs can be sufficiently low or even negative. As shown in (7), net CO2 emission EN,i,t equals to gross CO2 emission EG,i,t minus captured CO2 emission Eccpp,i,t. It’s obviously unreasonable to capture CO2 in the atmosphere, so the net CO2 emission is limited to be zero or positive. In this paper, we assume the tanks can store CO2 with max, OP imum PCEP during certain periods in total. , i, t 774

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participation factors s as shown in (13). It is important to note that participation factors s can be selected or optimized [21,22], however, that is not the focus of this paper.

G ⎧ EN , i, t = EG, i, t − Eccpp, i, t = eG × PC, i, t − αC × EP, i, t ⎪ EN , i, t ⩾ 0 ⎨ Eccpp, i, t + Sccpp, i, t − 1 = Sccpp, i, t ⎪ max ∀ i ∈ GCCPP ⎩ 0 ⩽ Sccpp, i, t + S0, i, t ⩽ Si

Δx = s (y s − y )

(7)

In practical operation, it’s obviously unrealistic to incorporate tanks with volumes that allow long-term storage. It’s necessary to ensure that the amount of CO2 stored in solvent does not exceed the capacity of the tanks.

4. Adjustable robust power dispatch model with CWSS and CCPPs under low-carbon economy In this section, we introduce the ARPD model with CWSS and CCPPs under low carbon economy.

3. Adjustable robust interval power dispatch

(a) Decision variables

In this section, the abstract adjustable robust power dispatch (ARPD) formulation with interval wind power is proposed.

Decision variables of the proposed ARPD model include:

(a) Brief formulation and solution

(1) The base power output of conventional units Pi,t (including normal conventional units, adjustable units and CCPPs) and wind power Pw,j,t; (2) The base power consumption of CCS, charging and discharging power of BES; (3) The allowable wind power generation interval [ y , y ], the adjusted power of adjustable units and BES. (b) Objective function

A robust power dispatch model with adjustable uncertainty intervals of wind power can be formulated as:

f (x , y, y , y ) ⎧ x , min y, y , y ⎪ x ⎪ s. t . [H , G] ⎡ y ⎤ ⩽ C , ⎣ ⎦ ⎨ ⎪x ⩽ x ⩽ x, y ⩽ y ⩽ y ⎪[ y , y ] ⊂ [ y , y ] ⎩

∀ y ∈ U (y , y )

T

(8)

t

N

⎩

N

∑ j j c wind [(Pw, j, t - Pw, j, t ) + ( Pw, j, t −

Pw, j, t )]

⎬ ⎭

The objective function of the low carbon economic dispatch model is to significantly reduce total operation costs, including power bidding costs (conventional units with and without CCS and wind power), CO2 emission costs (arising from low-carbon policy) and wind power curtailments costs by minimizing the difference between wind power forecasting intervals and allowed intervals as shown in (14).

(9) (c) Constraints for all wind power scenarios (1) Power balance constraints in base case: Total generation (conventional units and output of CWSS) and load (load and power consumed by CCS) are balanced at each time period t:

By introducing an auxiliary variable, (9) can be transformed as:

(Gi ( y + η (y − y )) ⩽ Ci ⎧ Hi x + ymax , y, y ⎨ s. t . 0 ⩽ η ⩽ 1 ∀i ⎩

(10)

Nj

Ni

Nc

BES ∑ Pi,t + ∑ (Pw,j,t − PcBES , j, t + Pd, j, t ) = Dt

The dual problem of Eq. (10) is:

i=1

j=1

+

∑ PCEP,i,t i

(15)

∀i (2) Generation output constraints of power units: Power outputs of conventional units (gross output for CCPPs) are within their technical limits shown in (16) and dispatched wind power cannot exceed the allowable interval shown in (17). Gcon and Gwind are the sets of conventional and wind power units.

(11)

From duality theory and according to [17], the two-layer problem can be expressed as:

Pi min ⩽ Pi, t ⩽ Pi max

min f (x , y , y ) x, y , y s. t . Hi x + Gi y + 1T βi ⩽ C

N

(14)

∀i

Hi x + Gi y + 1T βi ⎧ x ,min ⎪ y, y ⎨ s. t . βi ⩾ Gi (y − y ) ⎪ βi ⩾ 0 ⎩

N

i j i ⎧∑i = 1 (ci Pi, t ) + ∑ j c wind Pw, j, t + ∑i = 1 (cC EN , i, t ) + ⎫

∑⎨

min

The constraints should be held for any uncertain wind power output, and the optimized uncertainty interval [ y , y ] should be within the forecasting wind power interval [ y , y ]. In robust optimization, to guarantee the security for any wind power scenario, even for the worst-case scenario, the model is transformed into a two-layer model as follows [17]:

Gi y ) ⩽ Ci ⎧ Hi x + max( y ⎨ s. t . y ⩽ y ⩽ y ⎩

(13)

Pw, j, t ⩽

∀i

βi ⩾ Gi (y − y )

Pw, j, t ⩽ Pw, j, t ⩽ Pw, j, t ⩽ Pw, j, t

(16)

∀ j ∈ Gwind

(17)

(3) Ramping constraints:

βi ⩾ 0 x ⩽ x ⩽ x, y ⩽ y ⩽ y y ⩽ y, y ⩽ y

∀ i ∈ Gcon

(12)

(b) Adjustable strategy and variables

− Rampiu Δt ⩽ Pi, t - Pi, t − 1 ⩽ Rampiu Δt

∀ i ∈ Gcon

(18)

− Rampid Δt ⩽ Pi, t - Pi, t − 1 ⩽ Rampid Δt

∀ i ∈ Gcon

(19)

(4) Spinning reserve constraints: Upper and lower spinning reserves should be provided by conventional units to guarantee the operation reliability of the system in base case.

In this paper, several quick regulated conventional units are selected as adjustable units [20,21] and BES is also used to provide adjustable contributions to maintain power balance under worst-case scenarios. The power mismatches under worst-case scenarios are adjusted by adjustable conventional units and BES according to predefined

N

∑ [min(Pi max − Pi,t , Rampiu Δt )] ⩾ Rd i=1

775

(20)

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R. Zhang, et al. N

∑ [min(Pi,t − Pi min, Rampid Δt )]⩾Rd

u d u ⎧ Pi, t + Ai, t − Pi, t − 1 + Ai, t - 1 ⩽ Rampi Δt ⎨ Pi, t − 1 + Aiu, t − 1 − Pi, t + Aid, t ⩽ Ramp d Δt i ⎩

(21)

i=1

Pi, t + Aiu, t ⩽ Pi max

(5) Network constraints: The transmission limits are shown in (22). Generation shift factor GSFl-i in DC power flow model is introduced. N

∀ i ∈ Gadj (27)

∀ i ∈ Gadj

Pi, t − Aid, t ⩾ Pi min

(28)

N

Liml ⩽ ∑i =i 1 Gl − i × Pi, t − ∑b =b 1 Gl − b × Db, t +

(2) For BES, the power mismatch can be adjusted by reserved charging/ discharging abilities according to the participation factors sj,t as shown in (29). The BES should be operated within the limits as shown in (30) and (31).

N

BES ∑ j =j 1 Gl − j × (Pw, j, t − PcBES , j, t + Pd, j, t ) ⩽ Liml

∀ i ∈ Gcon

∀ j ∈ Gwind

(22)

(6) Rated capacity constraints of BES: The state of charge (SOC) of BES is calculated by (23) considering charging/discharging efficiency. The SOC of BES should be limited to its rated upper and lower capacity in (24). The total output of CWSS should be active as shown in (1).

PSOC , j (t ) = PSOC , j (t - 1) + ηc Pc, j, t − Pd, j, t /ηd

PSOC, j min ⩽ PSOC, j (t ) ⩽ PSOC, jmax

∀ j ∈ Gwind

∀ j ∈ Gwind

N

B jd, t = sj, t ∑ j =j 1 (Pw, j, t − B jc, t

(25)

N

N

N

i j u d ⎧∑i = 1 Ai, t + ∑ j = 1 B j, t = ∑ j =j 1 (Pw, j, t −

i

Pw, j, t )

(32)

(33)

i

(4) According to the method in Section ‘Adjustable Robust Interval Power Dispatch’, the positive/negative reserve constraints and positive/negative transmission limits can be transformed into (34)–(35) and (36)–(37) by introducing dual variables αj,t, βj,t, μl-j,t, πl-j,t.

⎧ ⎪

N

N

N

j BES BES ∑i =i 1 Pi, t − ∑i c PCEP , i, t + ∑ j = 1 (Pd, j, t − Pc, j, t )

N

N

N

+ ∑i =i 1 Aiu, t + ∑ j =j 1 Pw, j, t − ∑ j =j 1 αj, t ⩾ Dt ⎨ ⎪ − αj, t ⩽ Pw, j, t − Pw, j, t ∀ i ∈ Gadj ∀ j ∈ Gwind ⎩

(26)

D $35 400MW Sundance

$15 200MW A

(31)

Nj

Ni

E $10 600MW CCPP Brighton

$14 220MW

(30)

∀ j ∈ Gwind

∑ si,t + ∑ sj,t = 1

Pw, j, t ) ∀ i ∈ Gadj ∀ i ∈ Gadj

∀ j ∈ Gwind

⎨ ∑Ni Aid, t + ∑Nj B jc, t = ∑Nj (Pw, j, t − Pw, j, t ) j=1 j=1 ⎩ i=1 ∀ i ∈ Gadj ∀ j ∈ Gwind

(1) For adjustable conventional units, the upward adjusted power Aiu, t and downward adjusted power Aid, t are distributed according to the participation factors si,t as in (26). The adjustable units under worstcase scenarios should satisfy the ramping and generation constraints as in (27) and (28).

⎨ Aid, t = si, t ∑Nj (Pw, j, t − Pw, j, t ) j=1 ⎩

(29)

B jc, t )

(3) The total power mismatch under worst-case scenarios is adjusted by adjustable units and BES in (32). The sum of participation factors should be 1 as shown in (33).

In a robust optimization framework, solutions should be feasible under worst-case wind power scenarios. Problem (9) is a two-layer robust interval optimization model, and the constraints are linear. According to the method in Section ‘Adjustable Robust Interval Power Dispatch’ and [17], the worst-case scenario constraints are as follows:

N

∀ j ∈ Gwind

c d ⎧ ηc (Pc, j, t + B j, t ) − (Pd, j, t + B j, t )/ηd ⩽ ΔEc Δt ⎨ (Pd, j, t + B jd, t )/ηd − ηc (Pc, j, t + B jc, t ) ⩽ ΔEd Δt ⎩

(8) CCPPs constraints: Refer to (2)–(7). (d) Constraints under worst-case scenarios

u ⎧ Ai, t = si, t ∑ j =j 1 (Pw, j, t −

(Pw, j, t − Pw, j, t )

−(Pd, j, t + B jd, t )/ηd ⩽ PSOC, jmax

(24)

∀ j ∈ Gwind

Pw, j, t ) ∀ j ∈ Gwind

PSOC, j min ⩽ PSOC, j, t − 1 + ηc (Pc, j, t +

(23)

(7) Maximum charging/discharging constraints of BES constraints: The charging/discharging power in time period t is limited by its charging/discharging rates.

⎧ 0 ⩽ Pc, j, t ⩽ ΔEc Δt 0 P ΔEd Δt ⎨ ⎩ ⩽ d, j , t ⩽

=

N sj, t ∑ j =j 1

B

$30 420MW

C Solitude

Park City Fig. 2. PJM 5-bus system. 776

(34)

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⎧ ⎪ ⎨ ⎪ ⎩

N

N

There are two conventional units at Bus A (Park City). A CWSS including a wind farm with 450 MW capacity and BES with 300 MWh capacity is installed at Bus E, and its bidding cost is set to $5. The participation factor of BES is 0.2. ηc and ηd are 0.9. The hourly charged/ discharged limits are all 30% of the capacity and initial SOC is 100 MW. The load is distributed on three load buses. The lower generation limits of the conventional units are set to be 30% of their capacities. The generation unit at Bus E is assumed to be a CCPP, and units at Bus C and D are assumed to be adjustable units with the same participation factor s = 0.4. The maximum capture rate is set as 90%. ηccpp is set as 0.269 MWh/t CO2. The CCPP can capture CO2 at a maximum rate for 4 h. The upward and downward system spinning reserve rates are both set as 10%. The carbon tax is 20 $/t CO2. System loads are shown in Fig. 3.

N

j BES BES ∑i =i 1 Pi, t − ∑i c PCEP , i, t + ∑ j = 1 (Pd, j, t − Pc, j, t )

N − ∑i =i 1 Aid, t

βj, t ⩾ Pw, j, t −

+

N ∑ j =j 1

⩽ Dt

∀ i ∈ Gadj ∀ j ∈ Gwind

Pw, j, t

N

Pw, j, t +

N ∑ j =j 1 βj, t

N

(35)

N

i c b EP ⎧ ∑i = 1 Gl − i × Pi, t - ∑i Gl − b × PC , i, t − ∑b = 1 Gl − b × Db, t + ⎪ N Nj BES ∑ j =j 1 Gl − j × ( Pw, j, t − PcBES , j, t + Pd, j, t ) + ∑ j = 1 μl − j, t ⩽ Liml ⎨ ⎪ μl − j, t ⩾ Gl − j × (Pw, j, t − Pw, j, t ) ∀ i ∈ Gadj ∀ j ∈ Gwind ⎩

N

N

(36)

N

i c b EP ⎧ ∑i = 1 Gl − i × Pi, t − ∑i Gl − b × PC , i, t − ∑b = 1 Gl − b × Db, t + ⎪ N Nj BES ∑ j =j 1 Gl − j × ( Pw, j, t − PcBES , j, t + Pd, j, t ) − ∑ j = 1 πl − j, t ⩾ Liml ⎨ ⎪ πl − j, t ⩾ −Gl − j × (Pw, j, t − Pw, j, t ) ∀ i ∈ Gadj ∀ j ∈ Gwind ⎩

(37)

(1) Analysis of wind power dispatch

The ARPD model can be represented as (38), in which dual decision variables αj,t, βj,t, μl-j,t, πl-j,t are added. The two-layer robust optimization models are transformed into a single level LP problem, which can be solved with CPLEX.

min Eq (14) s. t . Eq (1) − (7) Eq (15) − (37) ⎨ ⎪α , β , μ , π j, t l − j, t ⩾ 0 ∀ j ∈ Gwind j , t l j , t − ⎩

Wind power forecasting errors are assumed to be 20% in this paper. Robust interval optimization results of wind power are presented in Fig. 4. In time periods 1, 2, 4–8, 10 and 16, the upper allowable wind power bounds are lower than the upper forecasting wind power bounds. The reason is that in those periods, if the forecasting wind power outputs equal to the upper forecasting values, wind power curtailment would occur. The upper allowable wind power outputs are determined according to load values. To maintain robust for worst-scenarios, the upper allowable wind power outputs are less than the upper forecasting wind power bounds in these periods. In all time periods, the lower allowable wind power bounds are the same as the lower forecasting wind power bound. The obtained allowable wind power interval is within the forecasting interval.

⎧ ⎪

(38)

5. Case studies In this section, the proposed adjustable robust optimization framework under low carbon economy with CWSS and CCPPs is performed on the modified PJM-5 bus system with one wind farm and the IEEE118 bus system with several wind farms. The ARPD model is solved using CPLEX [25] with Matlab on a PC with Intel Core i7 3.00 GHz CPU and 8 GB RAM.

(2) Benefits of CCPPs and BES To show the impact of CCPPs and BES on dispatch results, the following four cases are conducted. BES is not adjustable in these cases. Case 1: ARPD without considering BES and CCPP. Case 2: ARPD with CCPP.

(a) PJM-5 bus system The parameters of the PJM 5-bus system are from [26] (see Fig. 2).

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Fig. 3. System load of PJM-5 bus system. 777

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Upper Forecasting Wind Power

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Time (h) Fig. 4. Dispatched wind power calculated from robust interval optimization.

Case 3: ARPD with BES. Case 4: ARPD with BES and CCPP.

A comparison of the results of these four different cases is reported in Table 1. Overall cost is defined as the total cost considered in the objective function over the entire 24 h. The column of CO2 emissions shows that CCPPs can help to reduce the emission of CO2 while BES makes less contribution. It can be seen from the column of total dispatched wind power that the integration of either CCPPs or BES can contribute to the accommodation of wind power. When BES and CCPPs are combined to ARPD, the wind power can be dispatched at the highest rate. Because of the amount of the wind power that has been accommodated, the overall cost can be reduced for Cases 2, 3 and 4. Since ARPD with BES and CCPPs accommodate more wind power and CCPPs yield less CO2 emissions, Case 4 results in the least CO2 emissions, most dispatched wind power, and lowest costs. Please also note that if the

The dispatched wind power (or output of CWSS when BES is integrated) and output of Unit 3 for different cases are shown in Fig. 5. Unit 3 is one of the adjustable units, s of which equals to 0.5. Note that dispatched wind power in Case 4 is the largest comparing to other cases in most periods. For Unit 3, different amounts of dispatched wind power correspond to different output results. The output of Unit 3 in Case 4 is also the largest in most periods, because larger dispatched wind power decreases the upward adjusting requirement for adjustable Unit 3 (the difference between upper wind power interval and dispatched value decreases).

Wind Power (MW)

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Table 1 Comparisons of results under four cases. Cases

CO2 emissions (104 t)

Total dispatched wind power (103 MWh)

Total power output of Unit 1 (103 MWh)

Total power output of Unit 2 (103 MWh)

Total power output of Unit 3 (103 MWh)

Total power output of Unit 4 (103 MWh)

Total power output of Unit 5 (103 MWh)

Overall costs (105 $)

1 2 3 4

2.10 1.95 2.10 1.95

5.25 5.59 5.47 5.79

3.47 3.49 3.52 3.53

3.60 3.61 3.59 3.60

4.49 4.55 4.43 4.49

3.20 3.21 3.22 3.23

12.49 12.72 12.47 12.72

9.28 9.02 9.26 9.01

costs of Unit 3 and Unit 4 are high, more power has to be dispatched from the units corresponding to larger participation factors to provide adjustable capacities under worst-case scenarios.

wind power curtailment cost increases, the overall cost of Case 4 can be further reduced by its wind power accommodation ability. These observations suggest that the proposed model can help to develop low carbon economy. To further verify the benefit of BES, the SOC results of BES with participation factors s as 0, 0.2, 0.4 and 0.6 is presented in Fig. 6. When s is equal to 0, SOC has the largest variance, and the reason for that is that the BES is considered not adjustable. When s is positive, the corresponding BES is considered an adjustable resource, and a larger participation factor means more power mismatches caused by wind power uncertainty should be compensated by the BES before it reaches its operation limit. It can be seen from Fig. 6 that the SOC variances decrease with the increase of s. Moreover, the total utilized wind power corresponding to different s values are 5787.4 MWh, 5787.4 MWh, 5678.5 MWh and 5539.8 MWh. As the participation factor increases, the SOC variances and the amount of utilized wind power decrease. The reason is that the larger its participation factor is, the more ’charging/ discharging reserve’ BES must leave to be adjusted under worst-case scenarios. Table 2 lists the dispatching results of various CCPPs without BES for 24 h. Note that when the number of CCPPs in the system increases, the total CO2 emissions decrease, which verifies that the integration of CCPPs can directly contribute to CO2 emissions reduction. The overall costs during the dispatching horizon also decrease with the increase in the number of CCPPs (more captured CO2 and less emissions). It is worth noting that dispatched wind power increases when CCPPs are considered, but extra CCPPs (more than 2 in this case) cannot increase the amount of dispatched wind power anymore because the utilized wind power has reached the upper limit. Participation factors can influence the dispatched power of adjustable units. Unit 3 and 4 correspond to units at Bus C and D. Six subcases, cases 4.1–4.6 with different participation factors as shown in Fig. 7a), are conducted with the assumption that BES is not adjustable. The average output of adjustable units 3 and 4 are shown in Fig. 7b). The sum of participation factors of Unit 3 and Unit 4 equals to 1. Note that when the participation factor of Unit 3 or Unit 4 increases, the average output increases. In the PJM 5-bus system, since the bidding

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SOC (MWh)

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(b) IEEE 118-bus system The IEEE 118-bus system is applied to further demonstrate the applicability of the proposed model for large systems. This system consists of 118 buses, 54 generators, and 186 branches. The generator bidding data are similar to that in [27]. Five wind farms are connected at Busses 16, 37, 48, 75, and 83 with the half forecasting output the same as that in the PJM 5-bus system. Power units at Busses 12, 54, 59, 61, 66 and 69 are assumed to be CCPPs and units 5, 12, 21 and 40 are adjustable units with the same participation factors 0.2. The participation factors of the five BES are all set to 0.04. The hourly load is then multiplied by different factors to match the installed generation. In this subsection, we compare the ARPD model to the deterministic economic dispatch (DED) model. For the DED model, wind power is limited by its forecasting output and no uncertainties are considered. The objective function includes the first three items of (14), but the constraints under worst-case scenarios are ignored. The total operation cost of the ARPD model is $6.13 * 106, while the total operation cost of the DED model is $6.11 * 106. The utilized wind power and carbon emissions are almost the same for the two models. The slight increase in total cost for the ARPD model is caused mainly by the different dispatching results of adjustable units. Fig. 8 shows a comparison of the dispatched power outputs of the four adjustable units of the two models. Note that the dispatched power outputs of the corresponding units are the same in most time periods for the two models, i.e. the dispatched outputs of different units based on ARPD is almost as economic as the results from DED. The differences between the results from ARPD and from DED (e.g. unit 5 in periods 15 and 16, and unit 12 in periods 16 and 23, etc.) are due to the ability of ARPD to tackle wind power uncertainties. In other words, the solution of the ARPD model is conservative and the adjustable units must have enough reserves to ensure power balance under worst-case scenarios in certain time periods.

s=0 s=0.2 s=0.4 s=0.6

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Fig. 6. Exchanged power and SOC of BES with ranging participation factors. 779

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Table 2 Dispatch results with various CCPPs. CO2 emissions (104 t)

Total dispatched wind power (103 MWh)

Total power output of Unit 1 (103 MWh)

Total power output of Unit 2 (103 MWh)

Total power output of Unit 3 (103 MWh)

Total power output of Unit 4 (103 MWh)

Total power output of Unit 5 (103 MWh)

Overall costs (105 $)

0 1 2 3 4 5

2.10 1.95 1.88 1.80 1.77 1.72

5.25 5.59 5.59 5.59 5.59 5.59

3.47 3.49 3.57 3.64 3.65 3.67

3.60 3.61 3.63 3.72 3.76 3.80

4.49 4.55 4.57 4.58 4.59 4.60

3.20 3.21 3.20 3.21 3.21 3.22

12.49 12.72 13.00 13.27 13.40 13.57

9.28 9.02 8.93 8.82 8.78 8.72

participation factor

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Unit 3

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dispatched by adjusting the adjustable units and BES according to the corresponding participation factors. A trial is defined as successful if none of the generation limits, power flow limits, and BES operation limits are violated. The APRD model shows a 100% success rate for the 10,000 Monte Carlo trials, verifying that the proposed model can immunize the solution against wind power uncertainty. The results indicate that the proposed ARPD model makes the adjustable units operate to have more reserves under worst-case scenarios with only a slight cost increase, and immunizes the solution against the allowable interval wind power uncertainty set.

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6. Conclusion A novel adjustable robust power dispatch model with CWSS and CCPPs under low carbon economy is proposed in this paper. The structure of CWSS is presented to improve the operation flexibility of wind power, and the CCPPs are incorporated to reduce carbon emissions. Quick regulated units and BES are assumed to be adjustable with predefined participation factors under worst-case scenarios to make the solution feasible under wind power uncertainty. Aiming to provide a dispatch solution immunized against wind power uncertainty under low carbon economy, the ARPD model is formulated and transformed into an LP formulation based on interval wind power uncertainty. Allowable wind power intervals are also calculated and can provide reference to practice operations. Numerical cases show that the integration of BES and CCPPs can help to reduce wind power curtailments and carbon emissions. When the participation factor of BES increases, BES must leave more ‘charging/discharging reserve’ to be adjusted under worst-case scenarios. More CCPPs would reduce carbon

b)

Fig. 7. Participation factors and average output of adjustable units under different cases.

To further demonstrate the necessity of having reserves for adjustable units and the effectiveness of the proposed ARPD, a Monte Carlo analysis with 10,000 trials is carried out. In each Monte Carlo trial, a wind power output scenario is generated randomly based on the calculated allowable wind power interval. Then the system is re-

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emissions significantly and reduce overall costs. Numerical results on a larger system also verify that the proposed model can immunize the solution against the allowable interval wind power uncertainty set. In practice, the participation factors of adjustable units and BES should be allocated according to different operation conditions and price signals. Therefore, the future work of this paper involves constructing a more reasonable participation factors allocation method considering time varying operation conditions and price signals.

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