Optimal Operation of Distribution Network with ...

Preprints of the 18th IFAC World Congress Milano (Italy) August 28 - September 2, 2011

Optimal Operation of Distribution Network with Distributed Generations to Maximize Social Welfare M. Nikkhah Mojdehi, J. Zhang, X. Xia Department of Electrical, Electronic and Computer Engineering, University of Pretoria, Pretoria, South Africa. Abstract: Retail electrical power marketers, also known as retailers, typically set up contracts with suppliers to secure electricity at fixed prices on the one hand and with end users to meet their load requirements at agreed rates on the other hand. High penetration of distributed generation (DG) resource is increasingly observed worldwide. From the viewpoint of a retailer, this paper analyzes the problem of setting up contracts on both the supplier and end-user sides to maximize profits while maintaining a minimum operational cost of the distribution network with distributed generations. Proposed two-level optimization model in this paper, can minimize cost of distribution system with Distributed Generation and maximize profits of retailers. Numerical simulations are carried out based on an IEEE 33-bus test distribution network. Test results are included to show the performance of the proposed method. Keywords: Retailer profit, electricity market, wholesale market, distributed generation (DG), social welfare, distribution system, DisCo, distribution system operator (DSO). 1. INTRODUCTION Nowadays increasing demand of electricity forced power system operators to operate their systems close to thermal, mechanical and electrical limits. Several solutions could be considered to alleviate these operation conditions like increasing generation, transmission and distribution capacity, decreasing consumption by increasing equipments efficiency, demand management. These scenarios have their own advantages and disadvantages. Developments in distributed generation (DG) technologies, information and communication technologies, environmental concerns, liberalization in electricity markets and restructuring encourage using DGs in power system. Several definitions for distributed generations have been presented in the literature (Zareipour et al 2004 and IEEE 1547 Working Group 2003). This paper engages in the following definition: distributed generation is an electric power source connected directly to the distribution network or on the costumer side of meter (Ackermann 2007). The potential development of DG is sustained in the following factors: increasing power quality requirements, avoiding or shifting investment in transmission lines and/or transformers, minimizing ohmic losses, protecting the environment, and maintaining high energy prices at retail level (Ackermann et al 2000 and Sakis Meliopoulos 2001). Traditionally, a distribution company (DisCo) purchases energy from the wholesale market, at a high voltage level, and then transfers this energy to final customers. Nevertheless, the restructuring process of the energy sector has stimulated the introduction of new agents such as retailers and products, and the unbundling of traditional Copyright by the International Federation of Automatic Control (IFAC)

DisCo into technical and commercial tasks, including the provision of ancillary services 1 . Retailers purchase power from suppliers and sell it again to end-user customers. While there has recently been extensive research on market modeling at the wholesale level, the retail side and the reaction with DG has received relatively less attention. Gabriel et al. (2002) analyzed several strategies for determining forward loads for electrical power retailers based on empirically fit probability distributions for end-user loads and spot market prices. Contract design problem a retailer may encounter, both at the supply and end-user levels, was addressed by Gabriel et al (2006). It provides a stochastic programming methodology that allows the retailer to make informed contractual decisions, particularly in respect to contract prices and quantities. Yusta et al (2005) defined a model which can be applied to an energy service provider (which supplies electric energy for eligible industrial customers) in the Spanish electricity market. This model results in a quadratic non-linear optimization problem, where the objective function to be maximized is the economic profit obtained by the supplier, and it calculates the optimal electricity selling prices to be applied to the customers. The novel market integration mechanism was presented in Jimenez-Estevez et al (2007), which demonstrates that the design of a market interface and the consideration of DG units as equivalent power producers. The proposed scheme shows an adequate trade-off between technical accuracy (marginal cost theory and ohmic losses) and practicability (available network information and information management). Gordijn and Akkermans (2007) presented four models, based on sev1

International Energy Agency (2002). Distributed generation in liberalized electricity market.

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eral case studies, including distributed generation energy services to shift demand in peak hours (Spain electricity market), small-scale hydro plant as a local power producer (Norway electricity market), distributed generations in grid energy balancing (Netherlands electricity market) and distributed generations in active management of distribution networks (UK electricity market). Mashhour and Moghaddas-Tafreshi (2010) considered distributed energy resources in wholesale market to maximize their benefits using a multiperiod optimization model subject to operational and technical constraints. As mentioned before, DisCo, retailers, DGs and end users are participants in the distribution market. Relationships between these participants including money and power flow, operating of the whole system in respect to an objective function, suitable objective function which satisfies all participants and purchasing and selling price of electricity are still need to be studied. The goal of this paper is to find the sale price of retailers in the way that not only increases the profit of retailers but also develops social welfare. By social welfare we mean minimizing the cost of putting the distribution system into operation. This goal is implemented in a distributional network which in itself contains some distributed generation resources in a way that affects the mechanism of sale business. The costs will include the production cost of distributed generation units and the cost of purchasing from the wholesale market. To solve the above problem, an algorithm has been proposed which is implemented in two phases. The rest of this paper is organized as follows. In Section 2, we describe modeling considerations and Section 3 provides mathematical formulations for the simulation. Section 4 describes our numerical findings and is followed by the conclusions section. 2. RETAIL ELECTRIC POWER MARKET MODEL The model which is proposed in this section, considers two objectives. - The first one concerns minimizing the cost of distribution system operation, which is a problem that DisCo always experiences. It concerns how DisCo should use available resources to minimize the cost of distribution system operation. In the proposed model, it is assumed that available resources for Disco are distributed generations and purchased energy from retailers. - The second is about maximizing the retailer’s profit. It must be considered that the retailer’s profit be maximized. Retailers, on the one hand purchase power from wholesale market and distributed generation resources with spot prices considering the marginal cost of distributed generation units respectively, and on the other hand sell power to their final consumers with their expected sale price. The combination of these two pre-mentioned points formulates a solution in the way of achieving the expected results. The proposed method in this paper is based on a loop. In this loop, at first DisCo determines amount of available power from resources using economic dispatch to minimize the cost of distribution system operation.

Then retailers make their own strategy to buy electricity from available resources and sell it to their customers to maximize their profits. Meanwhile the goal of this paper is to find the sale price of retailers in the way that not only increases the retailer’s profit but also develops social welfare, minimizing the cost of distribution system operation. The costs will include the production cost of distributed generation units and the cost of purchasing from the wholesale market. So the profit of any retailer will be defined by: prof it = income − payment

(1)

In (1), income includes the input of each retailer based on the existing load of its customers and the tariff on which the contract is based. As it was mentioned in section 1 it is also assumed that in a distribution network the retailer contract with classes of the final consumers. These classes are usually classified in terms of their geographical positions. Payment will include the payout of each retailer to the power supplier with whom the named retailer contracts to provide the load of existing consumers in its own class. The resources from which the retailer in the distribution network can provide the power are the wholesale market and distributed generation resources. It is obvious that if there is no DG in the distribution network, the retailer will provide all the required power from the wholesale market with spot prices. But if there is any distributed generation units in the distribution network, then we will face a critical question and that is “what amount of required power would a retailer provide from the wholesale market and what amount will be provided from distributed generation units?” As a matter of fact the combination of the retailer’s purchase from the wholesale market and the distributed generation units would be in a way to increase retailer’s profit. But would this be advantageous for the final consumer? To answer all these questions, in the following an algorithm is proposed to reach the maximum social welfare. 3. MATHEMATICAL FORMULATION As it was mentioned earlier, the presence of distributed generation resources in the distribution network will bring about some ambiguities concerning the payout of the retailer and the purchasing strategy carried out by them. To remove these ambiguities an algorithm is proposed in this paper that will be accomplished in two phases. In the first phase of this proposed algorithm an optimal power flow will be administered from the distribution system operator (DSO) point of view, in a way that the cost of power production in the distribution system must be minimized. By using this method the production portion of each distributed generation unit and the power injection portion from the wholesale market to the distribution network classes will be determined. The optimization model of this optimal power flow (minimization of operation cost of the whole distribution system) is as follows:

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min

" n 24 X X t=1

c=1

LoadN c,t Pn ∗ P ricec ∗ PW,t N Load c,t c=1


# m X + CDGi,t (Pi,t ) ,

subject to: (2)

i=1

Loadc,t =

subject to: PW,t +

m X

Pi,t = Ploss,t +

n X

LoadN c,t ,

(3)

LoadN c,t

¸ · βc (P ricec − P riceN c ) , (7) ∗ 1+ P riceN c

Loadc,t = PWc,t +

c=1

i=1

(4) Pi,t ≥

≤ Pi,t ≤

Pimax ,

(5)

for all t = 1, . . . , 24, i = 1, . . . , m, k = 1, . . . , M , and in which n denotes the total number of classes; t is the time from 1 to 24; LoadN c,t is nominal power demand of class c in hour t; PW,t is the injected power from the wholesale market at hour t; P ricec shows the price of electrical energy sold to class c; Ploss,t is real power loss in distribution network at hour t; Pi,t is power generation of DG at hour t; m and M are total number of DG units and nodes in the distribution network respectively; Vk,t shows 2 voltage of node k at hour t, CDGi,t (Pi,t ) = ai Pi,t + bi Pi,t + ci defines the cost characteristic of DG i at hour t. In (2), optimization variables are PW,t and Pi,t . The first term in the optimization model (2) represents the costs of energy purchasing from wholesale market, and the second term represents the generation costs for distributed generation units. Constraints (3), (4) and (5) represent the load balance of the whole distribution network constraint, voltage constraint on every node of the distribution network and generating limits which are specified as upper and lower limits for the real power outputs of DG units, respectively. Relationships between voltage of nodes and injected power to the network, including wholesale market and DGs, can be found in Nikkhah Mojdehi et al (2009). In the beginning of implementing this algorithm in the first phase, we do not have any access to the price of classes; therefore we need to assume the initial values to determine the price of the classes. At the first iteration it is assumed that the price of the classes equals the spot price of the wholesale market, so a preliminary value for the generation of distributed generation units and the injection power from the wholesale market will be achieved. Using these initial values, the algorithm will enter in its second phase. In this phase, the main goal is to maximize the profit of retailers in a way that the income of selling electricity to classes be maximized and at the same time costs related to purchasing electricity from the wholesale market with spot price and purchasing from scattered resources with limited prices of these production units are minimized. By fulfilling this part, the price of electricity will be measured in each class. The optimization model in this part is as follows: " n 24 X X max Loadc,t ∗ P ricec − t=1

n X m X c=1 i=1

c=1

M CDGi,t ∗ PDGi,c,t −P ricespot,t ∗

PDGi,c,t ,

(8)

i=1

Vkmin ≤ Vk,t ≤ Vkmax , Pimin

m X

n X c=1

# (6) PWc,t ,

n X

PDGi,c,t ,

(9)

c=1

PW,t ≥

n X

PWc,t ,

(10)

c=1

for all t = 1, . . . , 24, c = 1, . . . , n, i = 1, . . . , m, and in which PDGi,c,t denotes the power purchased by a retailer of class c from the distributed generation unit i (DGi ) in hour t; M CDGi,t = 2 ∗ ai PDGi,c,t + bi defines the marginal cost of distributed generation unit i in hour t; P ricespot,t shows the spot price of the wholesale market in hour t; PWc,t is the power purchased by a retailer of class c from the wholesale market in hour t; Loadc,t denotes the real load of class c in hour t; βc is the load elasticity class c; P riceN c shows the nominal sale price of class c; P ricec represents the sale price of class c. The first term in the optimization model (6) represents the income of energy selling of each retailer corresponding to their classes, the second term is the cost of purchasing energy from distributed generation units and the third term represents the cost of purchasing energy from the wholesale market. In (6), optimization variables are P ricec , PDGi,c,t and PWc,t . Constraints (7) and (8) represent the end user demand function and the load balance of each class respectively. Constraints (9) and (10) guarantee that summation of purchased power from each DG and wholesale market by retailers is less or equal to the dispatched power of each DG and wholesale market by DSO (Pi,t and PW,t ). Kirschen (2003) and Boisvert et al (2002) presented one of the existing and most useful models of the function of price response of loads of network. This demand function shows how load changes in respect to variations in electricity prices. In (7) the load function is in linear form based on nominal variables. In this equation P riceN c is the selling price of the nominal electrical power consumed. It is assumed that (in the situation of nominal demand LoadN c,t ) the retailer sells electricity at a price which is 10% higher than the whole cost, that is, it assigns a profit on income of 10%. In this equation it is assumed that the response of each consumer to the price variation, characterized by the elasticity β , has to be empirically assigned. The price elasticity of demand, β, measures the degree of response of the demand to the changes of price in the market, being defined as the ratio of the variation of the demand quantity of some commodity or service, in percent, to the variation of its price P rice , also in percent. It can be expressed as: ∆Load/Load β= . (11) ∆P rice/P rice

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Fig. 1. Demand function

Fig. 2. Daily load variation

The demand is “elastic” if β is higher than 1, and “inelastic” if β is lower than 1. Some studies has been performed to characterize the end user response to several price strategies 2 3 , elasticity values ranging from -0.01 to -0.25 have been chosen. Corresponding to Fig. 1 elasticity value is determined by a negative value and equals to -0.2. After implementing the optimization model in phase two, the sale price in each class will be achieved. Then these results will be applied to optimal power flow in phase one as input. After optimal power flow in phase one, the amount of economical generation from distributed generation units and amount of injection power from the wholesale market are determined. Then these economical power generation and injection from optimal power flow in phase one are applied to optimization problem of phase two as inputs in order to calculate the selling prices. Until converging, the sale price of each class must be iterated. Using the proposed algorithm, it can be seen that without load elasticity, retailer’s sale price will increase sharply. On the other hand, load elasticity regulates sale prices and limits retailer’s profit. 4. SIMULATION AND NUMERICAL RESULTS An IEEE 33-bus distribution system (Choi et al 2003), is used to illustrate the proposed model and solution algorithm. Maximum and minimum limitation for voltage is assumed 0.9 and 1 pu, respectively. The system includes four distributed generation units at nodes 4, 7, 25 and 30, three retailers. DG technologies considered in this paper are Fuel Cell-CHP (FCC), Gas ICE-CHP (GIC), Gas ICE-Power only (GIP), Microturbine-CHP (MC) and Microturbine-Power only (MP). Subsequently there will be three classes of retailing in the mentioned system. Table 1 shows the cost characteristics of varieties of DG unit technologies considered in this work 4 . In this system the number of each load will be determined by the number of the node attached to it. Table 2 shows the load classification based on the classes.

Fig. 3. Spot price of wholesale market during a day The assumed time interval for simulations is 24 hours a day. Fig. 2 and Fig. 3 show the load variations and spot prices of the wholesale market during a day respectively. From Fig. 4 to Fig. 6, it can be seen that the retailer of each class tends to supply the demand of its class from the wholesale market principally. Also it can be concluded that the retailer’s strategy is approximately constant with applying different distributed generation technologies and because of high consumed power in each class, retailers prefer to use this units in off peak hours rather than peak hours. Table 1. Distributed generations data with varieties of technology DG Technology FCC GIC GIP MC MP

a 0.0001 0.0001 0.0001 0.0001 0.0001

b 0.0315 0.0374 0.0777 0.0421 0.0841

c 1.0749 0.4777 0.3483 0.5553 0.4603

Pmax 400 400 400 400 400

Pmin 0 0 0 0 0

Table 2. Load classifications

2

Joskow P. and Tirole J. (2004). Retail electricity competition. CSEM working paper., University of California Energy Institute, Tech. Rep., 130. 3 Available at http://www.cne.es. 4 Available at http://www.cbo.gov.

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Retailer’s Class A B C

Loads 2, 3, 4, 5, 6, 19, 20, 21, 22, 23, 24, 25 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18 26, 27, 28, 29, 30, 31, 32, 33


Fig. 4. Purchasing strategy of retailer of class A, with Fuel Cell-CHP technology

Fig. 7. Total profit of each retailer with several DG technologies

Fig. 5. Purchasing strategy of retailer of class B, with Gas ICE-CHP technology

Fig. 8. Price of each retailer with several DG technologies Also from Fig. 7, it can be found that the retailer of class A has higher profit because of higher demand of its class than the others. More loads for the retailer do not lead to more profit and the retailer’s profit is affected by load forecasting. More loads are equal to more load forecasting error which can decrease the retailer’s profit significantly.

Fig. 6. Purchasing strategy of retailer of class C, with Microturbine-Power only technology Fig. 7 shows that the retailer’s profit without using distributed generation resources is increased and out of evaluated technologies in this paper, Gas ICE-Power only and Fuel Cell CHP have the highest and the lowest profits for retailers respectively.

Simulation results are come from this fact that the retailer’s cost is composed of two parts. The first one is the cost of purchasing power from the wholesale market which is actually the purchased power multiplied by the price of the wholesale market which is constant during an hour and therefore the retailer’s strategy relevant to this price will not be complicated. The second part of the retailer’s cost is the cost of purchasing power from distributed generation resources which includes purchased power from these units multiplied by their marginal cost. It is worth to mention that the purchasing price (i.e. the marginal cost) from these units depends on its active generation power and is a linear curve with a positive slope. On the other hand, increase in power purchased from these units leads to higher price of these units therefore the cost of purchasing power from these units is increased. In comparison it should be mentioned that increase in purchasing power from the wholesale market leads to a lower purchasing

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power than the power supplied by distributed generation resources mostly because of constant prices. An important point from these results is the retailer’s income which includes the price of each class multiplied by the load of its class. As illustrated in Fig. 8 the retailer’s price is constant during a period and dose not respond to hourly variations in wholesale prices and it results to uneconomical signal 5 , so retailers look for suitable profit margin with lower cost and higher income. 5. CONCLUSIONS From simulation results, can be seen that in this modle, retailers tried to purchase electricity from DGs. It means that it can be considered as incentives for DGs owners to invest. The following conclusions can be drawn from this paper: - Retailers can experience the most profit without using distributed generation resources but their profits associated with distributed generation units are maximized with Gas ICE-Power only technology. - In this paper, determination of optimal purchasing strategy and the retailer’s profit maximization is implemented with social welfare maximization. - Without applying subsidiary budget from governments, distributed generations cannot be supported by retailers. - In general terms, the more elastic the behavior of customer demand, the lower the profit obtained by retailers, as customers have an increased response capacity to price changes. On the other hand, most of the inelastic customers will tolerate price increase without reducing considerable consumption, and thus generate more revenues and higher profits.

Gabriel S. A., Conejo A. J., Plazas M. A., and Balakrishnan S. (2006). Optimal price and quantity determination for retail electric power contracts. IEEE Transaction on Power Systems, 21, pages 180–187. Yusta J. M., Ramirez-Rosado I. J., Dominguez-Navarro J. A., and Perez-Vidal J. M. (2005). Optimal electricity price calculation model for retailers in a deregulated market. International Journal of Electrical Power and Energy Systems, 27(5-6), pages 437–447. Jimenez-Estevez G. A., Palma-Behnake R., Torres-Avila R., and Vargas L. S. (2007). A competitive market integration model for distributed generation. IEEE Trans. Power Systems, 22, pages 2161–2169. Gordijn J., Akkermans T. (2007). Business models for distributed generation in a liberalized market environment. Electric Power System Research, 77(9), pages 1178–1188. Mashhour E., Moghaddas-Tafreshi S. M. (2010). Integration of distributed energy resources into low voltage grid: a market-based multiperiod optimization model. Electric Power System Research, 80(4), pages 473–480. Nikkhah Mojdehi M., Kazemi A., and Barati M. (2009). Network operation and reconfiguration to maximize social welfare with distributed generations. EUROCON, pages 552–557, St.-Petersburg. Kirschen D. S. (2003). Demand-side view of electricity markets. IEEE Trans. Power Systems, 18, pages 520– 527. Boisvert R. N., Cappers P. A., and Neenan B. (2002). Demand-side view of electricity markets. IEEE Trans. Power Systems, 18, pages 520–527. Choi J-H., Kim J-C., and Moon S-I. (2003). Integration operation of dispersed generations to automated distribution network for network reconfiguration. Proc. Conf, IEEE Power Technologies Conference, Bologna, Italy, June 23–267.

REFERENCES Zareipour H., Battacharya K., and Canizares C. A. (2004). Distributed generation: current status and challenges. 36th Annual North American Power Symposium, pages 1–8, Idaho, Aug. 9–10. IEEE 1547 Working Group (2003). P1547 standard series for interconnecting distributed resources with electric power systems. Technical Report. Ackermann T. (2007). Distributed resources and reregulated electricity markets. Electric Power System Research, 77(9), pages 1148–1159. Ackermann T., Andersson G., and Sder L. (2000). Electricity market regulations and their impact on distributed generation. Electric Utility Deregulation and Restructuring and Power Technologies, pages 608–613, London, U.K., Apr. 4-7. Sakis Meliopoulos A. P. (2001). Distributed energy source: needs for analysis and design tools. IEEE Vancouver Summer Meeting, Vancouver, BC, Canada. Gabriel S. A., Genc M. F., and Balakrishnan S. (2002). A simulation approach to balancing annual risk and reward in retail electrical power market. IEEE Transaction on Power Systems, 17, pages 1050–1057. 5

Holtz-Eakin D. (2003). Prospects for distributed electricity generation. The Congress of the United States [online], Available: http://www.cbo.gov.

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