Locational Marginal Price for Distribution System Considering Demand Response

Locational Marginal Price for Distribution System Considering Demand Response Farshid Sahriatzadeh, Pramila Nirbhavane and Anurag K. Srivastava The School of Electrical Engineering and Computer Science Washington State University Pullman, WA, USA Abstract With ongoing smart grid activities, more amount of information is available from end-users. Objective is to use this information to make power system more efficient, environmental friendly, reliable, and secure. Major part of smart grid investment is going towards distribution systems. One of the goals within smart grid is development of infrastructure to avail price signal to end users in distribution system. This price signal is currently based on rough estimate of nodal price in transmission system. Transmission nodal price does not reflect fair pricing signal for distribution system without consideration of distribution system constraints. Solving optimal power flow (OPF) with applicable constraints is necessary to obtain locational marginal price (LMP) for each node that can be used in real-time pricing (RTP). Formulation and implementation of distribution LMP (DLMP) is needed for fair pricing. In this work, DLMP formulation is developed consisting of three major parts similar to that of LMP in transmission system but implemented at distribution level. Also, price responsive load brings another interesting prospective of demand response (DR) as shown in results. Effect of DR on DLMP using 12 bus distribution system has been presented. I. INTRODUCTION Smart grid activities will help in monitoring and managing the electricity flow from generation sources to meet the varying load demands in better way. Smart grid will enable the coordination of the generators capabilities and meet needs of the end users within electricity market to optimize the utilization of the resources in best possible way. This will lead to minimizing both costs and environmental impacts while maintaining system reliability and security. Pricing mechanism is very significant for successful operation of electricity market. Electricity prices generally fluctuate between low-demand hours and high-demand hours throughout a day. The emerging technology such as installation of smart meters and application of real time pricing (RTP) leads to better energy management technologies and hence overall welfare. Real-time price is an expected electricity rate which varies with time in order to reflect the electric utility's time varying costs of generation, transmission, and distribution [1]. Using RTP based on the supply conditions, customer can change the power consumption. This may provide a significant contribution in decreasing the price hikes and price volatility. RTP can also reduce the occurrence of system shortages and blackouts as demand can respond as reserve margin. The idea of spot pricing for utilities was first put forth by William Vickrey [2] in 1971. He suggested the real-time pricing of electric power and allowing the retail customer to react. He postulated that utilities could minimize the peak usage and use congestion driven rates to invest in new capital investments. The idea was further developed by Bhon, Caramanis, and Schweppe [3], in 1984 and they proposed a methodology which considered the marginal price of energy, losses, and congestion to determine the spot prices. LMP represents the marginal cost to supply an additional increment of power to the location without violating any system security limits [4]. LMPs are calculated generally every 5 minutes on a real time market, for every bus in the system above certain voltage [5]. LMP consists of three major components, cost of energy, cost of losses, cost of congestion, and it can accommodate other factors and constraints such as environmental impact or harmonic injection [6-7]. There have been suggestions on applying nodal pricing to the distribution network. Currently distribution system has flat price based on transmission nodal price. The flat rate-retail system causes market inefficiency [8]. Various approaches have been proposed to determine the nodal prices in a distribution network. The LMP for distribution network would represent the real-time cost of supplying power at any point in the distribution network and would provide fair support mechanism to the renewable energy generation. For analyzing DLMP, it is decomposed into three components, marginal energy cost (MEC), marginal loss cost (MLC) and marginal congestion cost (MCC). The price is determined at every node of the distribution system. Optimal power flow on an AC system is used to determine the DLMP. The aim of this paper is to study and formulate the DLMP to maximize the social welfare for both the demand and supply with consideration of demand response. Maximizing the social welfare is calculated using. This is executed on a 12- bus distribution system. To study the effects of demandresponse on the system considered, some loads are made price responsive. The DLMP calculation is developed in MATLAB environment based on optimal power flow solver from MATPOWER 4.0 simulation package [9]. 978-1-4673-2308-6/12/$31.00 2012 IEEE

II. PROBLEM FORMULATION The AC OPF model can provide more accurate results since it solves for losses and reactive power. Due to its relatively slow speed, AC OPF is not necessarily the typical model for transmission simulation. However, in a distribution system, this model should compute very fast and without much convergence problem. A generic formulation can be formed as [10]: ( ) ( ) Where ( ) ( ) (1) (2) (3) ( ) (4) In this form, social welfare function will be maximized to obtain DLMP by computing the Lagrangian multiplier of the real power equality constraint of (2). Because the DLMP will be interfacing with the transmission LMP, the transmission LMP is a natural starting point for the creation of a DLMP. Using price responsive load OPF formulation will be able to handle demand response cases. In the AC OPF formulation, the objective function is representing the system cost, (2) and (3) include the nodal real and reactive power balancing equations respectively, (5), (6) and (7) are the constraints on generations and bus voltages respectively, (4) is branch flow constraint which is obtained from thermal limit. Bounds in inequality constraints are typically supplied by unit commitment and security analysis tools in real-time system operations. In the electricity market, cost function is not in the form of quadratic cost because it does not cognitively match how market participants want to trade in the real world. Instead, non-differentiable piecewise cost based on offers and bids is (5) (6) (7) adopted for better pricing transparency and flexibility. For example, assuming only real energy cost is considered, the objective function can be written as given in [11]. ( ) { ( ) [ ( )]} { } where and represent offer prices, and are the real power output levels at various breakpoints on the piecewise price curve ( ) based on offer, is clearing real power, NB is the number of real power blocks offered to the market from a given generator, and m is by definition the block index that satisfies. Costs for reactive energy, voltages, and other more complex resources and services can take similar forms. Because of the piece-wise form of bid functions, derivatives of Lagrangian changes abruptly around breakpoints. To deal with type of functions in OPF problem, Wang et al [11] explained three approaches; Trust-Region based Augmented Lagrangian Method (TRALM), Step- Controlled Primal-Dual Interior Point Method (SCIPM), and Constrained Cost Variables (CCV) Formulation. III. CASE STUDY Meng and Chowdhury [10] proposed a simple 12-bus distribution system shown in Fig-1 to implement DLMP algorithm. The system configuration is symmetrical. The system is connected to the grid at buses 1 and 10. Buses 3, 6, 8, and 11 are conventional PQ buses each with loads of 200kVA with 0.7 lagging power factor; and buses 2, 5, 9, and 12 are solid state transformer (SST) nodes each with a load of 50kW. Because of SST, power factor on these buses is unity. The designated distribution system may draw energy from the main grid during contingencies such as DG shortage, line outages or congestion. The DLMPs will be calculated as Lagrangian multiplier of equation 2 for each bus in distribution system. In this work, end-user loads contribute in total value of cost function through demand response program. In equation 1, ( ) is benefit of customer bid in the market which enable proposed algorithm to deal with demand response in the distribution market. Demand Response (DR) can be defined as the changes in electric usage by end-use customers from their normal consumption patterns in response to changes in the price of electricity over time. Further, DR can be also defined as the incentive payments designed to induce lower electricity use at times of high wholesale market prices or when system reliability is jeopardized [12]. There are several general actions by which a customer response can be achieved. Each of these actions involves cost and measures taken by the customer. In this work, we assumed that responsive loads can (8)

TABLE I 12 BUS DISTRIBUTION SYSTEM DATA DISTRIBUTION SYSTEM DATA VOLTAGE BASE( kv ) V 12 MVA BASE (MVA) B S B 1 z 0.896 j0. L 0. I max 270A FEEDERS IMPEDANCE 7743 FEEDERS LENGTH ( mile ) 5 FEEDERS THERMAL LIMIT BUS Specifications DG Installation 2 P B2 =50 kva, p.f. = 1.0 P S2 =350 kva 3 P B3 =200 kva, p.f. = 0.7 (lagging) - 5 P B5 =50 kva, p.f. = 1.0 P S5 =350kVA 6 P B6 =200 kva, p.f. = 0.7 (lagging) - 8 P B8 =200 kva, p.f. = 0.7 (lagging) - 9 P B9 =50 kva, p.f. = 1.0 P S9 =350 kva 11 P B11 =200 kva, p.f. = 0.7 (lagging) - 12 P B12 =50 kva, p.f. = 1.0 P S12 =350 kva set their consumption in between of their max and min bounds. There are several general actions by which a customer response can be achieved. Each of these actions involves cost and measures taken by the customer. In this work, we assumed that responsive loads can set their consumption in between of their max and min bounds. IV. SIMULATION RESULTS AND DISCUSSION A- Case 1: Base case In this case the generation values assigned to the DGs are sufficient to satisfy all demand needs. The total supply value of the generation is 1050kW. The total bid quantity is 760kW with no elasticity to the loads and loads having maximum possible demand. Optimal power flow is performed on a generic AC model. The results are shown in Table II. It can be seen that there is no congestion in this scenario. To maximize the social welfare all generations are dispatched based on offer prices. In AC power flow due to the losses in the network, S2 and S12 balance the losses by generating more power. This adds to the marginal cost values in each bus and gives a higher value of DLMP. As AC OPF is not lossless, we can see in the result that system has total 60kW loss. In this case, line flow limits are not applied so there is no congestion in the system. It can see from the result that S12 is marginal generation. The social welfare of base case is 21.4$. B- Case 2: With responsive load It can see from the results of case 1 that all loads are at their maximum capacity. Adding responsive load can take DR into account. We are expecting loads change if they can set their consumption with respect to the price signal. In this case, we assume loads at bus 3, 6, 8, and 11 as price responsive. They can vary in their limit (maximum of 140 kw and minimum of 0 kw) as they have in the Table I. As results are shown in Table III, load at bus 3 reduced its consumption. Bus No. TABLE II AC OPF RESULT OF BASE CASE DG DG DLMP ($/MWh) 1 58.259 1000 0-2 55.000 280 240 50 3 60.360 - - 140 4 58.041 - - - 5 46.666 400 320 50 6 54.763 - - 140 7 56.286 - - - 8 57.768 - - 140 9 55.908 250 100 50 10 51.841 1000 0-11 61.781 - - 140 12 57.495 220 150 50 Fig. 1. Base case power flow for 12 bus system In Table II, it has been shown that bus 3 is the highest DLMP among buses 6, 8, and 11. As it was expected, load at higher DLMP tends to decrease its consumption. Also, marginal generation is S2 in this case, while it was S12 for base case (case 1). As we do not have any limit on line flow, there is no congestion on the lines. Social welfare in this case is 22.12$. Also in this case social welfare and DLMPs increases because of responsive load. C- Case 3: Congestion on feeder 11-12 It is observed from case 2 that line 11-12 has highest flow in the network. So the line limit of 11-12 is arbitrary reduced to 40kVA to create congestion on this line. The AC OPF results in the presence of responsive loads show that congestion causes power injection reduction from 12. Therefore, S2 increases its output to pick up the extra demand and became marginal seller. Another interesting result is related to responsive loads. As responsive load at bus 3 increases its demand 10kW in compare with case 2, responsive load at bus 11 decreases its demand 40kW as this bus became marginal price among responsive loads.

Bus No. TABLE III AC OPF RESULT OF CASE 2 DLMP DG DG ($/MWh) 1 76.330 1000 0-2 74.493 280 100 50 3 75.757 - - 90 4 70.844 - - - 5 63.738 400 200 50 6 69.625 - - 140 7 67.017 - - - 8 67.159 - - 140 9 61.012 250 250 50 10 65.444 1000 0-11 78.113 - - 140 12 70.005 220 200 50 Bus No. TABLE IV AC OPF RESULT OF CASE 3 DLMP DG DG ($/MWh) 1 83.516 1000 0-2 75.00 280 200 50 3 75.011 - - 100 4 68.431 - - - 5 62.391 400 200 50 6 68.020 - - 140 7 68.356 - - - 8 65.936 - - 140 9 60.00 250 240 50 10 64.155 1000 0-11 92.517 - - 100 12 65.00 220 70 50 Fig. 2. Case 2 power flow for 12 bus system As shown in the Table III and Table IV, maximum DLMP increase in the case 3 and minimum DLMP decrease in the case 3, in comparison with case 2 as expected, since system is more stressed; however, increase in DLMP due to line congestion is not so much compared to result based on [10], due to the presence of price responsive loads. Based on [10], maximum LMP obtained through AC OPF in same 12 bus system with same congested line has increased by 99 percent in compare with case 1 in [10]. However, in the presence of DR it has increased only by 18 percent in compare with case 1. The social welfare of case 3 is 20.3$, reduced due to congestion leading to re-dispatch in the distribution system, so the expensive seller becomes marginal. Congestion can island part of network from available source and cause higher price. D- Case 4: Increasing fixed load level In this case congestion is removed, but all fixed loads increase two times of their previous value. As it is mentioned in the [10], increasing loads makes all generators to work at their maximum capacity. However, in this case because of responsive loads, it is possible to not buy power from grid that is most expensive seller. Fig. 3- Case 3 power Flow for 12 bus system As it is expected, responsive load decreases its consumption while DGs increase their generation. In compare with case 2, total load and total generation increased but generations are below their limits. Social welfare in this case is 29.14$ which increased significantly in compare with case 2, and it was expected because fixed loads are increased. AC OPF result is shown in Table V for this case. Bus No. TABLE V AC OPF RESULT OF CASE 4 DLMP DG DG ($/MWh) 1 78.609 1000 0-2 75.000 280 210 100 3 78.255 - - 60 4 77.795 - - - 5 78.706 400 200 100 6 83.682 - - 140 7 78.696 - - - 8 81.221 - - 110 9 74.985 250 250 100 10 79.985 1000 0-11 82.377 - - 140 12 76.465 220 220 100

Fig. 4. Case 4 power Flow for 12 bus system In the fig- 5 variation of price due to different conditions in four cases for all 12 buses are shown. As discussed, price is higher in the presence of demand response, however; demand response make system flexible against congestion. As shown by results, making congestion on line 11 to 12 didn t change price signal on other buses drastically. Fig. 5. Variation of DLMP in different scenarios for 12-BUS system Although existing responsive load in the system leads to higher DLMP as shown in fig- 5, it saves total energy usage. It can be seen from fig- 6 that highest energy sold is for case 4 which loads increased. For three cases with the same amount of load, lowest energy sold belongs to case 3 which has congestion on the line 11 to 12, and also case 2 which has DR, consumes lesser energy in compare with case 1 which does not have DR. V. CONCLUSIONS Formulation for distribution locational marginal price has been developed with consideration of demand response in this paper. Developed algorithm has been applied to several test case scenarios for example test system. Price responsive loads bring interesting features and can reduce the effect of congestion and peak load as shown in simulation results. This work can lead to suitable benchmark for future studies on DLMP for the distribution system within smart grid. Implementing market in distribution networks needs more study and elaborated algorithms to take all constraints into account will be part of future work Fig. 6. Total DG energy sold in 4 study cases ACKNOWLEDGMENT The authors are thankful to financial support provided by the School of Electrical Engineering and Computer Science as well as Research Office at Washington State University for this work. REFERENCES [1] B. Chapman, T. Tramutola, "Real-Time Pricing: DSM at its best? The Electricity Journal, v. 3, no. 7, August-September 1990, p. 40-49. [2] W. Vickery, Responsive Pricing of Public Utility Services, The Bell Journal of Economics and Management Science, vol. 2, no. 1, pp. 337-346, Spring, 1971. [3] R. Bohn, M. Caramanis, F. Schweppe, Optimal Pricing in Electrical Networks Over Space and Time, The RAND Journal of Economics, vol. 15, no. 3, pp. 360-376, Autumn, 1984. [4] Xu Cheng, Thomas J. Overbye. An Energy Reference Bus Independent LMP Decomposition Algorithm, IEEE Trans., vol.21, no.3, Aug. 2006. [5] H. Daneshi and A. K. Srivastava, ERCOT Electricity Market: Transition from Zonal to Nodal Market Operation, IEEE Power and Energy Society General Meeting, 2011. [6] M. Baughman, S. Siddiqi, J. Zarnikau, Advanced Pricing in Electricity Systems Part I: Theory, IEEE Trans. Power Syst., vol. 12, pp. 489-495, Feb. 1997. [7] M. Baughman, S. Siddiqi, J. Zarnikau, Advanced Pricing in Electricity Systems Part II: Implications, IEEE Trans. Power Syst., vol. 12, pp. 496-502, Feb. 1997. [8] S. Borenstein, S. Holland, On the Efficiency of Competitive Electricity Markets with Time-Invariant Retail Prices, The RAND Journal of Economics, vol. 36, no. 3, Au-tumn, 2005. [9] R.D. Zimmerman, C.E. Murillo-Sanchez, and R.J. Thomas, MATPOWER: Steady-state Operations, Planning and Analysis Tools for Power Systems Research and Education, Power Systems, IEEE Trans., vol.26, no.1, pp. 12-19, Feb. 2011. [10] F. Meng and B. H. Chowdhury, Distribution LMP-Based Economic Operation for future Smart Grid, Power and Energy Conference at Illinois (PECI), Feb., 2011. [11] H. Wang, C. E. Murillo-Sanchez, R. D. Zimmerman, and R. J. Thomas, On Computational Issues of Market-Based Optimal Power Flow, IEEE Transactions on Power Systems., vol. 22, no. 3, pp. 1185 1193, Aug. 2007. [12] US Department of Energy, "Benefits of Demand Response in Electricity Markets and Recommendations for Achieving Them, Report to the United States Congress, February 2006. Available online: http://eetd.lbl.gov.