Day Ahead Scheduling of Distribution System With Distributed Energy ...

Day Ahead Scheduling of Distribution System With Distributed Energy Resources Considering Demand Response and Energy Storage Mojtaba Khanabadi, and Sukumar Kamalasadan, Power, Energy and Intelligent Systems Laboratory (PEISL) Department of Electrical and Computer Engineering University of North Carolina at Charlotte Charlotte, NC-28223, USA

Abstract— This paper propose a method for day-ahead optimization of distribution system with Distributed Energy Resources (DER’s) and energy storage devices that allows a) increase market efficiency and b) damping the variations of DER’s. The objective is to utilize energy storage to damp the variations in the grid considering market price and to increase the grid efficiency. First, the implementation of day-ahead optimization that will determine which generation unit including DER’s should be utilized using next 24 hour load taking into consideration of renewable energy generation forecasting is discussed. Next, the utilization of energy storage to damp the energy variations in the grid is evaluated. The problem is formulated as Nonlinear Programming (NLP) with the objective of maximizing the social welfare of the grid. The results shows that the proposed method can successfully fulfill the overall objectives.

N OMENCLATURE Indices i, j t n, ng , nd

Index for Bus. Index for hours. Number of buses, generators and loads, respectively.

Variables PDG,i,t , QDG,i,t

DG’s active and reactive power generation at Bus i at Time t. PW M,i,t , QW M,i,t Active and reactive power purchased from system at Bus i at Time t, respectively. Active and reactive power interchanged PN D,i,t , QN D,i,t from system at Bus i at Time t, respectively. Up Dn , ΔPDG,i,t positive slack variables for DG’s generΔPDG,i,t ation variations at Bus i at Time t. Up Dn ΔPW M,it , ΔPW M,it positive slack variables for purchased energy from Wholesale market at Bus i at Time t, respectively. S Schedule Storage capacity at Bus i at Ei,t Time t. O Operational Storage capacity at Bus i at Ei,t Time t. Apparent power flow at Line i-j. Sij

978-1-4799-1255-1/13/$31.00 ©2013 IEEE

V i , δi S S , PDS,i,t PCS,i,t O O , PDS,i,t PCS,i,t

Parameters CC, i, t ex Pd,i,t

PD,i,t , QD,i,t PW F,i,t max max , Vi,t Vi,t max Sij

RU Pi,t , RDNi,t ηCS , ηDS ρDG,i,t , ρW F,i,t ρW M,i,t , ρN D,i,t Matrices Y ∈ Rn×n θ ∈ Rn×n

Voltage magnitude and angle at Bus i. Charging and discharging rate of schedule storage at Bus i at Time t. Charging and discharging rate of operational storage at Bus i at Time t. Constant operating cost at Bus i at Time t. Expected demand participation in DR program at Bus i at Time t . Active and reactive power demand at Bus i at Time t. Wind farm active power generation at Bus i at time t. Upper and lower bounds for voltage magnitude at Bus t at Time t. Upper bound for apparent power flow at Line i-j. DG’d up and down ramp rate limits. Charging and discharging efficiency of Storage. DG and wind farm operation cost, respectively. Wholesale market and neighboring Disco energy price. Network admittance matrix. Angle matrix of admittance matrix. I. I NTRODUCTION

Now a days Distributed Energy Resources (DER’s) are becoming more and more prominent in the power grid especially in the power distribution systems. However the integration of DER’s with renewable energy resources makes the operation of the grid more complex due to the variability and unpredictability. Also, in the presence of Demand Side Management strategies, integration of DER’s with renewables can have a

negative effect if an optimal method considering market price has not been deployed. However, current distribution network has not been designed for connecting highly dense DER’s with renewable resources. It is important that the distribution network should be an active network in order to integrate high level of DER’s. Active distribution network is defined as a network which not only have DGs units, energy storages and controllable loads (DERs) but also include a optimal power management method that allows these device add value to the system at multiple levels including ancillary services [1].Our hypothesis is that a day ahead scheduling of power distribution system with near real-time optimization that can damp the energy variations in the grid and/or increase markets efficiency is going to be an important factor for efficient operation of the power grid with highly dense DER’s. Such scheduling of energy at the distribution level considering market interactions, demand response, energy storage and DER forecasting at the Distribution Management System (DMS) will be one important factor that allows to transform passive distribution network to an active one. In order to maximize participation of the consumers to the DR program, improving the relation between power generators and consumers is very important [2]. However, utilizing renewable energy resources is not a secure way to meet the loads due to uncertainties and stochastic nature of such generations. During past several years several studies have been performed utilizing demand response and DERs in the grid to convert the distribution system as an active grid. The authors in [3] and [4] considered some methods to provide incentives so that costumers will participate in the demand response program. However, just using DMS programs will not be sufficient to fulfill the overall objectives of making the grid an active one. Studies have also been performed to have an active and efficient power grid with energy storage [5] and [6]. Integration of customer driven Demand Response (DR) program with highly volatile DER’s with renewable energy resources is a significant and complex energy management task [7]-[9]. Damping energy variations is one of the challenges that should be addressed before changing current distribution network to the active one. In this paper, a method is developed by which energy storage has been used to damp the grid power variations that has been created by the wind generation units and demand response program. This method is then integrated with respect to market pricing and energy exchange in response to wholesale market. The paper is organized as follows. Section I provide a literature review and the main objective of the work, Section II discusses main concept and system model for implementing proposed method. Section III illustrates main results and discussions. Section IV conclude the paper. II. C ONCEPTIONAL F RAMEWORK In the restructured power system, the independent system operator (ISO) will play the role of the wholesale market. Generally Distribution Companies (DISCO’s) forecast the load

consumption for the next 24 hour in their networks and send this data to the wholesale market. Based on the forecasted load in the whole system, system operator will run Security Constraint Unit Commitment (SCUC) to find optimum unit commitment of the system with respect to system security criteria and find market clearing price (MCP). Further, this signal price will be sent for the market participation decision that include industrial costumers and DISCOs. If were to include active resources in the power distribution system, the distributed system operator (DSO) should run another unit commitment and optimization algorithm to meet the internal loads within the DISCO based on DG’s operational cost, wholesale price signal and system operation cost. This internal optimization may be run based on Demand Response (DR) program if customer participation based on pricing should be included. In the customer participation program, participating costumers have contract with DSO that they will decrease their energy consumption by specified percentage during the peak hours and/or increasing their energy consumption during some specific hours.The results of internal DISCO’s unit commitment determine that which unit and when that unit should be utilized to minimize system’s operation cost. Moreover, the amount of energy that have to be purchased from the wholesale market will be determined based on this commitment. Figure 1 illustrates the algorithmic flow chart and the schematic diagram of the proposed architecture, respectively. However, due to stochastic nature of wind generation and DR program, the energy variations will appear in the system. This coupled with load changes and scheduling based on customer DR programs can significantly affect the system balance. For example, in some hours the provided energy may be higher than real load and in some other may be lower than real value of the load. Thus an operational storage and a dispatchable storage should be considered to damp the energy variations in the system and increase the system efficiency. With such a strategy we propose two different type of energy storage system with two different functionality. One of them will be dispatched for next 24 hours using the optimization data (grid level storage) and another one will be charged and discharged using real-time optimization to damp the energy variations. In addition, demand response program will be used to increase system efficiency when the energy price is high and if there is a need to purchase more energy from wholesale market. Based on the proposed methodology we will consider three different case: • •

•

Base case: No operational storage bank and no DR program is used but grid level storage is deployed. Operational Storage: Utilizing dispatchable storage bank to damp the system’s energy variation without DR program. Storage and DR program: Utilizing operational storage and DR program to damp the energy variations.

We will now discuss the problem formulation for the proposed optimization architecture.

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Overall algorithmic framework for the proposed method.

TABLE I

(1)

S.t. PW M,i,t + PDG,i,t + PW F,i,t + PDS,i,t − PCS,i,t − Pd,i,t nd  = |Vi,t | |Vj,t | |Yi,j | cos(δj,t − δi,t + θi,j ) j=1

(t = 1, 2...., N T )

(2)

QW M,i,t + QDG,i,t − Qd,i,t = nd  |Vi,t | |Vj,t | |Yi,j | sin (δj,t − δi,t + θi,j ) − j=1

(t = 1, 2...., N T )

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Fig. 1.

market operating cost as the input.

(3)

2) Generation limits: Each DG unit cannot provide power more than its maximum limit and violate its upper and lower ramp rates. Moreover the active power that can be purchased from wholesale market is limited: min max ≤ PDG,i,t ≤ PDG,i,t PDG,i,t

(4)

max 0 ≤ PW M,i,t ≤ PW M,i,t

(5)

max Qmin DG,i,t ≤ QDG,i,t ≤ QDG,i,t

(6)

PDG,i+1,t − PDG,i,t ≤ RU Pi,t

(7)

PDG,i−1,t − PDG,i,t ≤ RDNi,t

(8)

DG’ S O PERATION C OST α($/M W h) β($)

DG7 20 15

DG12 25 17

DG15 26 18

DG24 28 22

A. First Level: Conventional Optimization with Dispatchable Energy Storage

In this case, based on the predicted load and wholesale market price for next 24 hour the DSO will run a conventional AC optimal power flow (ACOPF) with energy storage. The proposed, grid level storage will be used to store the energy (charged) when the price is low and be utilized (discharged) when the price is high. Using this method, the DSO would be able to decrease system operating cost. Overall ACOPF formulation for base case without utilizing operational storage bank and DR program is discussed here. DG’s cost multipliers are shown in Table I. Following equations illustrates the overall formulation: 1) Power flow equations: At the DISCO level, the objective is to minimize the total operational cost including Dispatchable Generators (DG), wind farm, storage considering wholesale

3) System Security limits: Voltage level at system’s buses cannot hit upper and lower limits. In addition, the power flow in the lines is restricted. min max ≤ Vi,t ≤ Pi,t Vi,t

 max   Sij,t ≤ Sij,t

(9) (10)

4) Energy Storage Model: The amount of active energy that is available in the energy storage is modeled using the following equations. This amount is dependent on available energy at previous period and the value of charging and/or discharging rate at previous period. E(i, t + 1) = E(i, t) + PCS,i,t ×ηCS − PDS,i,t × ηDS (t = 1, 2, ...., N T ) (11) min max ≤ Ei,t ≤ Ei,t Ei,t

(12)





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Example 32 bus distribution system for analysis.

max 0 ≤ PCS,i,t ≤ PCS,i,t

(13)

S Dn PW M,i,t − ΔPDG,i,t ≥ 0

max 0 ≤ PDS,i,t ≤ PDS,i,t

(14)

3) Operational Storage Model: Operation storage model is the same as in the previous case with the difference that this energy storage will be used in real time optimization.

B. Second Level: Optimization and Scheduling Utilizing Operational Energy Storage As discussed in previous section, in this case, the operational storage bank is utilized to damp the variations that may happen in the system. The formulation for this case is as follows: 1) Objective Function: The objective is to minimize the amount of control actions that the system operator have to perform to damp the variations. In should be noted here that this optimization will be performed after base case optimization. It means that the results of this optimization is completely dependent on previous case results. 24   ng

M in

Up Up Dn Dn ΔPW M,i,t + ΔPW m,i,t + ΔPDG,i,t + ΔPDG,i,t

t=1 i=1

(15) 2) Power Flow and Generation Limits: Power flow limits and generation limits have to be modified as illustrated below: S S R S S PW M,i,t + PDG,i,t + PW F,i,t + PDS,i,t − PCS,i,t − Pd,i,t Up Up Dn Dn O ΔPW M,i,t + ΔPW m,i,t + ΔPDG,i,t + ΔPDG,i,t + PDS,i,t nd  O − PCS,i,t = |Vi,t | |Vj,t | |Yi,j | cos(δj,t − δi,t + θi,j ) j=1

(t = 1, 2...., N T )

(16)

Up S max + ΔPDG,i,t ≤ PDG,i,t PDG,i,t

(17)

S Dn max − ΔPDG,i,t ≥ PDG,i,t PDG,i,t

(18)

Up S max PW M,i,t + ΔPW M,i,t ≤ PW M,i,t

(19)

(20)

O O ×ηCS − PDS,i,t × ηDS E O (i, t + 1) = E O (i, t) + PCS,i,t

(t = 1, 2, ...., N T )

(21)

O,min O,max O Ei,t ≤ Ei,t ≤ Ei,t

(22)

O,max O ≤ PCS,i,t 0 ≤ PCS,i,t

(23)

o,max O 0 ≤ PDS,i,t ≤ PDS,i,t

(24)

other constraints are (3), (6)-(10). III. I MPLEMENTATION M ETHOD AND C ASE S TUDY For discussion and for illustration purpose a modified version of the 32 bus radial test system are used [10]. This system contains four DGs, two wind farms and one storage bank consisting of two individual storage units. The overall one line diagram is as shown in Fig. 2. Hourly load and wind power forecasted are available as in reference. Moreover, it is assumed that distribution system can purchase active energy from wholesale market. The case is tested on a 2.5-GHz, 6-Gb RAM personal computer and CONOPT solver is used to solve the problem. A. Base Case results The results of applying proposed method for the base case is discussed here. The system operator will buy energy from the wholesale market and use DGs only when their marginal price is lower than wholesale market price. Figure 3 shows DGs schedule for the next 24 hour based on forecasted load and expected price (Fig. 5) for next 24 hour. Moreover, The results

Power (MW)

bus7 bus15

1

2

3

bus12 bus24

4

5

Fig. 3.

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Hour

DGs schedule for next 24 hours based on forecasted load and price.

TABLE II DG’ S GENERATION VARIATIONS AND GRID IMPACT DUE TO OPERATIONAL

Hour 9 Hour 10 Hour 11 Hour 12 Hour 13 Hour 15 Hour 17 Hour 19

Bus 7 (KW) 0 0 0 0 0 0 -0.492 -0.093

Bus 24 (KW) 0.027 0.233 0.629 0.041 0.549 -0.425 0 0

Without Operational Storage With Operational Storage

24 Exchanged Power (MW)

STORAGE

22 20 18 16 14 12 10 1

indicate that during the night, when the energy price is low, the dispatchable level storage will be charged and discharged during day the (Fig. 5).

7

9 11 13 15 17 19 21 23 Hours

Energy Variation at Dispatchable Storage

Stored Energy (MW)

As discussed, distribution system operator schedule the resources to meets the load with minimum operation cost based on the day ahead market price and forecasted load. However, in the real operation of the grid loads and generation may change. Therefore, the system operator should utilize the resources to damp variations. Under such scenario normally, system operators try to buy/sell more energy from/to wholesale market which may lead to higher cost. Here, we try to damp such variations using operational storage bank without DR program. The extra storage will be charged or discharged only during the real time operation of the grid. When the generation is higher than the load the storage will be charged to reduce or relieve the generation burden at the grid level. On the other side, when the load is higher than generation we do not need to buy more energy from wholesale market or utilize expensive DG as the storage will discharge its energy to the grid (Fig. 6). Therefore, system operator may not need to buy more energy from the grid (Fig. 4). Table II shows the changes in DG’s variation after utilizing Operational storage to damp the energy variations.

5

Fig. 4. Power exchanged between distribution network and wholesale market.

2.5

B. Damping variations using operational storage bank

3

Wholesale Energy Price

35

2

30

1.5

25

1

20

0.5

15

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4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

10

0 1 3 5 7 9 11 13 15 17 19 21 23 Hour

Fig. 5. Energy variation in the dispatchable storage; Expected wholesale market price for next 24 hours.

C. Utilizing storage bank and demand response In this test case, it is assumed that 10 out of 32 loads already participate in the demand response (DR) program. Also, each load in the DR program can decrease it’s consumption by 3 percent of the scheduled consumption. Keeping the same objective function and corresponding constraints as in the previous subsection, the expected load consumption will be calculated using: Ex S ≥ (1 − K) Pd,i,t Pd,i,t

(25)

1 Fig. 6.

3

5

7

9 11 13 15 17 19 21 23 Hour

The energy variation in operational storage at Bus 16.

Hour 1 Hour 2 Hour 3 Hour 16 Hour 18 Hour 20 Hour 24

Bus 7 (KW) 0 0 0 0 -0.595 -0.206 -0.052

2 1.5 1 0.5 0

-0.5

1

3

5

7

9 11 13 15 17 19 21 23 Hour

Fig. 7.

The energy variation in test case.

IV. C ONCLUSION

TABLE III DG’ S GENERATION VARIATION DUE TO OPERATIONAL STORAGE AND DR Wholesale Market (KW) -0.402 -0.127 -0.741 0 0 0 0

Without Operational Storage and DR (Base Case) With Operational Storage, No DR With Operational Storage and DR

2.5 Energy Variation (MW)

Stored Energy (MW)

With Operational Storage, No DR With Operational Storage and DR

1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0

Bus 24 (KW) 0 0 0 -0.515 0 0 0

It is worth mentioning here that one of the most important role of the DR program is to damp the energy variations in the grid. However, in most cases DR cannot fully optimize the system and relieve energy variations. Therefore, using (15)(25), we use operational storage to augment the DR program. The results indicate that effective management of extra storage and DR is a better and efficient way to damp the variations in the grid and as such effectively managing storage and DR simultaneously produce better results than having only the DR program. With the proposed method system operator may not need to purchase additional energy from wholesale market at spot price condition. Moreover, it has been found that during some hours of the day, system operator can decrease power generation from expensive DG’s (Table III). Figure 7 compares the energy variations for different cases. Due to stochastic nature of the load, the real load can change during successive intervals while performing real-time optimization. Operation storage let us damp such energy variations in the system. In a system with DR, one can find that when we add operation storage to the DR program the energy variations is higher than the case where we use operational storage without DR (1.41MWh in this example). However, when compared to the base case (Fig. 7) it can be seen that the system operator can sell 1 MWh energy to the spot market. The extra revenue can be dispersed between costumers who participate in the DR program in the form of the incentives. It should be noted here that the rest of the energy variation is due to losses in distribution and transmission lines.

In this paper a novel method using real-time optimization is proposed for relieving energy variations in the power grid especially in the presence of DG’s and renewable energy resources. The proposed method consider two different energy storage types and uncertainties in renewable energy resources. The results indicate that the proposed optimization methodology can successfully manage the grid in the presence of renewable eenrgy resources, other form of distributed generation and market transactions with the overall objective of improving system efficiency and operational value. Moreover, it is shown that using storage types at various levels in the power grid(operational and dispatchable in this study) the architecture allows higher efficiency and economic value even in the presence of DR program. R EFERENCES [1] P. S. M. Braun, “A review of aggregation approaches of controllable distributed energy units in electrical power system,” International Journal of Distributed Energy Resources, vol. 4, no. 4, pp. 297–319, 2008. [2] “Benefits of demand response in electricity markets and recommendation for achieving them,” US Department of Energy, Report to the United State Congress, Feb. 2006. [3] K. Hamilton and N. Gulhar, “Taking demand response to the next level,,” IEEE Power Energy Mag, vol. 8, no. 3, pp. 60–65, May 2010. [4] P. Palensky and D. Dietrich, “Demand side management: Demand response, intelligent energy systems, and smart loads,” IEEE Trans. Ind. Informat., vol. 7, no. 3, pp. 381–388, feb 2011. [5] Barton, “Fast model predictive control using online optimization,” Control Systems Technology, IEEE Transactions on, vol. 18, no. 2, pp. 267 –278, march 2010. [6] J. Mattingley, Y. Wang, and S. Boyd, “Code generation for receding horizon control,” in Computer-Aided Control System Design (CACSD), 2010 IEEE International Symposium on, sept. 2010, pp. 985 –992. [7] S. Salinas and M. L. amd Pan Li, “Multi-objective optimal energy consumption scheduling in smart grids,” Smart Grid, IEEE Transactions on, vol. 4, no. 1, pp. 341–348, 2013. [8] I. Atzeni, L. Ordonez, G. Scutari, D. Palomar, and J. Fonollosa, “Demand-side management via distributed energy generation and storage optimization,” Smart Grid, IEEE Transactions on, vol. 4, no. 2, pp. 866 – 876, 2013. [9] K. Tanaka, K. Uchida, K. Ogimi, T. Goya, A. Yona, T. Senjyu, T. Funabashi, and C.-H. Kim, “Optimal operation by controllable loads based on smart grid topology considering isolation forecasted error.” Power Systems, IEEE Transactions on, vol. 2, no. 3, pp. 438–444, 2013. [10] M. Doostizadeh and H. Ghasemi, “Day-ahead scheduling of an active distribution network considering energy and reserve markets,” Electric Power, European Transactions on, vol. 19, doi: 10.1002/etep.1630 2012.