Impact of Photovoltaic Distributed Generation on Generation Resource Allocation

Transcription

1 th Hawaii International Conference on System Sciences Impact of Photovoltaic Distributed Generation on Generation Resource Allocation Insu Kim 1, Miroslav Begovic 1, Hyunju Jeong 2, John Crittenden 2 1 School of Electrical and Computer Engineering, 2 School of Civil and Environmental Engineering Brook Byers Institute of Sustainable Systems, Georgia Institute of Technology, Atlanta GA, USA Abstract Various aspects of electricity generation resource allocation and planning are presented in this study on a hypothetical example of the generation resource pool of the state of Georgia augmented by a substantial amount of photovoltaic renewable generation, likely to happen in the next several years due to increased proliferation of PV, supported by both technological advances (higher efficiency cells) and economic benefits (lower prices due to the economics of scale). 1. Introduction Photovoltaic (PV) systems have for years been considered an emerging technology, mostly due to high production costs of the primary materials (mostly crystalline silicone). Due to a variety of factors, both technical and economic, the industry achieved tremendous growth in recent years. In 2011, 2.6 GW of additional capacity was installed in the United States alone. Other countries, especially European, are promoting renewable generation technologies, including PV, very aggressively. Even though PV accounted for about 1 percent of the renewable generation mix in the United States in 2011 (heavily dominated by hydro and wind), it was lately growing at 105 percent year-to-year. Under such circumstances, grid parity will not be far out, as the economy of scales involved in PV production suggests that every worldwide doubling of the manufacturing production results in the `net 20 percent reduction of the system cost. It is not unreasonable to expect that, depending on the economic conditions, grid parity will be reached across the world by the end of the decade (as it depends on local solar yield, as well as local prices of the utility generated electricity, it is a highly location-sensitive quantity and has taken a long time to come within reach, especially in the countires bulk power electricity generation is large scale and inexpensive, as it is in the United States). In the late 1960 s, several states in the US began imposing constraints on electricity generation emissions such as sulfur dioxide (SO 2 ), nitrogen oxides (NO X ), and carbon dioxide (CO 2 ). In 1990, the Clean Air Act amendments emphasized environmental issues of the release of pollutants and greenhouse gases into the atmosphere. In addition, since the advent of increased proliferation of mostly smaller capacity, low cost distributed generation (DG), photovoltaic (PV) systems began to be incorporated into power systems in larger quantities. The increased presence of renewable generation (with its inherent low cost and stochastically available resources) is a mixed bag of benefits, offering some opportunities (peak load shaving, effective loss reduction due to the proximity of generation and loads, potential to be used for volt/var management and control, etc.), but also creating new problems (need for additional spinning reserve to cover the uncertainties involved in the inputs). According to some exchanges on popular engineering internet discussion boards, like Power Globe, operating low cost, conventional fossil fuel plants continuously at full capacity over a period of time instead of ramping down and up to allow generation by intermittently available renewables may actually increase the fossil fuel consumption of the plants! While such assertions are largely in the domain of hearsay, the problems associated with needs for spinning reserve are real and need to be addressed, as the penetration of renewables in modern smart grids is getting increasingly large. This calls for analysis of resource scheduling and dispatch at utility level, which has traditionally been developed for nonstochastic, non-renewable resources whose operational costs depend on the fuel consumption and location of the plant in the electrical network. Many analytical techniques deal with fuel costs and emissions as constraints. One of the techniques is to minimize a cubic objective function with the constraints of fuel costs and emissions such as SO2 and NOX by /12 $ IEEE DOI /HICSS

2 using the Lagrange multiplier method [1]. Another approach is based on the stochastic formulation method that examines the uncertainties in the system production cost and load demand via multiple runs [2]. In the study, the trade-off relationship between the conflicting objectives was simulated by the weighted sum method [2]. In addition, many studies introduced the genetic algorithm [3, 4] and evolutionary programming [5] to solve the problem of the noncommensurable objective function. Recently, another approach presented the method simulating social behavior such as particle swarm optimization [6] and bacterial foraging optimization [7]. However, these studies do not address the ecological impact of water. Energy and water infrastructures are tightly linked in production and consumption, in some cases with direct links. With increasing awareness about the need for sustainability of energy and water infrastructures, this link may require to add the water consumption constraint to the objective function. Therefore, this study presents a resource allocation algorithm with the scalar mixed-objective function that merges fuel costs, emissions, and water consumption constraint. We test the algorithm using several one-year simulations of the generation resource pool of the state of Georgia enhanced by a substantial additional PV capacity likely to happen in the next decade. In addition, this study analyzes the long-term effect of renewable DGs on the entire grid. Section 2 introduces the general theory on resource allocation, such as emissions modeling, hydroelectric coordination, and the dispatch strategy; Section 3 presents the example of the state of Georgia, which requires load consumption modeling, water inflow modeling, head rates, and renewable energy generation of the state of Georgia; Section 4 shows results of energy savings, cost savings, the PV generation cost, and the minutely simulation; Section 5 provides a summary of major points. 2. Generation Resource Allocation 2.1 Emissions Modeling The input-output model of a generating unit that burns fossil fuel can be formulated as a polynomial function of its power output [1] ( ) = + + ( ) = = + + P Gi = net power output in MW F i = fuel input of i th generating unit in MBtu/hr C i = total operating cost in $/hr f pi = equivalent fuel price of i th generating unit in $/MBtu. The emissions output of SO 2, NO X, CO 2, and water from the generation unit can be approximately correlated with fuel consumption., ( ) =, =, +, +,, ( ) =, =, +, +,, ( ) =, =, +, +,, ( ) =, =, +, +, ef i = emission factor in kg/mbtu or gallons/mbtu EO i = emission output in kg/hr of SO 2, NO X, and CO 2, respectively WO i = water output in gallons/hr. 2.2 Hydroelectric Unit Modeling The input-output model of a hydroelectric unit for constant head can be approximated by a first-order and second-order equation [8]. = ( ) = + 0, [ /] + +, <, q = water flows in acre-ft/h P H = net hydroelectricity output in MW. Fig. 1 The hydroelectric unit input-output characteristics with the constant head The model presented here relates water reserves and their usage for hydroelectric production, which is capable of serving as a quick and effective support of other renewable resources, prone to random and somewhat unpredictable changes in output (i.e., hydro resources can act as part of the spinning reserve). This paper does not address the problem of spinning reserve from the operational standpoint and remains at the level of hourly scheduling of generation resources. 2.3 Allocation Strategy (1) Steam Turbine Generation For N generating units, the objective function can be formulated as follows: subject to q in acre-ft/h [ ( ) + ( )] P Hi,saddle P H in MW

3 = +,,. P Load is system load and P Loss is transmission or distribution losses which are expressed by the loss coefficient matrix [9]. The losses are calculated by solving power flow equations of real power constraints and reactive power constraints. As losses are important, but non-essential for the objectives of this study, we elect to consider them constant and focus on the resource part of the model. The conclusions drawn are mostly not impacted by this simplification. The Lagrangian function can be represented by = ( ) + ( ) +( = Lagrangian multiplier N= total number of generators. Optimal solution to the constrained problem can be found from Kunn-Tucker conditions. The optimal Lagrangian multiplier is found by the iterative bisection or secant search. The procedure for obtaining the optimal solution continues to iterate until an acceptable tolerance is met. (2) Hydrothermal Coordination The optimal coordination of the hydroelectric generation unit requires more complex procedure than thermal units satisfy hydraulic as well as thermal unit constraints. The coordination problem can then be formulated as follows: subject to ( ) ( ) = + +, =, + =0, = n i = number of hours in the i th interval F i = fuel input of i th generating unit in MBtu/hr q i = water discharge in the i th interval in acre-ft/hr q Tot = total water discharge P Si = thermal unit generation in the i th interval P Hi = hydroelectric unit generation in the i th interval T = total interval. ) Furthermore, it is assumed the distance between the hydroelectric unit and the load to be very short. The electrical losses are [8] = (3) Objective Function The objective function is defined to minimize costs and emissions with appropriately chosen weight coefficients, W. Linear combination of costs and emissions is formulated as: [ ] =1. {,,,,} The optimal dispatch algorithm minimizes the objective function with linear combination of costs and emissions. The concept of the Pareto-optimal solution set for the four-dimensional, non-scalar objective function is shown in Fig. 2. The figure indicates that the most minimum-cost points are located around the maximum-emission points. This suggests that the objective function proposed in the study correlates well with the Pareto-optimal solutions. Fig. 2 Pareto-optimal solutions for four-dimension objective function 3. Example The purpose of the study is to analyze impact that significant presence of renewable energy generation, photovoltaic systems in this case, would have on the operational costs of the entire grid. We choose to model load consumption data approximately, by typical load profiles. Load profiles for typical residential, commercial, and industrial customers in 2010 are obtained from the actual utility data [10]. The load profiles are synthesized from actual net generation which in 2010 was 125,538 GWh [11], and the number of customers as of December 31, 2010, which totaled 2,361,355 in the residential, commercial, and industrial customer type [12]. Fig. 3 shows the duration curve of the approximate load consumption of the state of Georgia with GW at peak and 125,538 GWh in net generation

4 Fig. 3. Approximate load consumption of the state of Georgia in GW For hydrothermal coordination, we model the water inflow data. Nineteen active hydroelectric plants constitute two percent of the energy mix of Georgia [12]. Daily water inflow data are approximated by the Bartletts Ferry hydroelectric plant, which provides daily inflow data from 1997 to The hydroelectric plant supplies percent, of the hydroelectricity net generation of Georgia. Fig. 4 shows the duration curve of the approximate water inflow data with 164,923 peak inflow in acre-ft/day and 30,954 minimum inflow in acre-ft/day. Fig. 4. Approximate water inflow of the state of the Georgia in acre-ft/day The heat rates of the modern thermal unit ranges 8.6 to 10 MBtu/MWh [13] or 9.8 to 11.4 MBtu/MWh [8] with overall efficiencies between 30 to 35 percent [8]. To assess impact of significant presence of renewable photovoltaic (PV) systems, we assume that all PV systems are distributed across the representative six locations in Georgia. We also assume that PV systems generate a total of 10 percent of the peak load capacity. It is assumed all the PV systems are oriented with 0 azimuth angle and 30 tilt angle. To analyze the impact of PV systems on the state grid, we propose a resource allocation algorithm to be applied to the entire system. The detailed simulation plan is shown in Table 1. PV generation is assumed to consist of a large number of relatively small systems totaling 10, 20, or 30 percent of the peak load, while a coal, gas-fired, nuclear, and a hydroelectric generation power plants constitute 67, 10, 21, and 2 percent respectively of the energy mix, supplying a total demand of 125,538 GWh/year. The minimum and maximum limits, and the ramp rates for different generation types are presented in Table 1. Ramp rates for coal-, gas-fired, and nuclear generation are 0.005, 0.04, and PU/min, respectively. Because every utility maintains spinning reserve for unexpected situations, we assume that whenever demand exceeds 95 percent of daily peak, additional ten percent of spinning reserve capacity is deployed to cope with unanticipated contingencies. The ten percent spinning reserve is modeled by the peaking generation of gas turbines. The cost functions for these small gas turbines are randomized as follows: ( ) = (1+ ) =(0,0.2), =(0,0.1), =(0,0.001) and (0, ) is a normally distributed random variable with zero mean and standard deviation, = 1,,. Table 1. Capacity information for the generation mix of the state of Georgia (including hypothetical PV system penetration of 10 percent installed in six locations). Type Energy mix Capacity limit in GW Cost [12, 14] $/ MWh 10% of peak PV 3.8 GW 10% Atlanta(36.52%), Augusta(17.03%), Columbus(16.51%), Savannah(11.85%), Athens(10.15%), Macon(7.94%) Min Max Coal 67% Gas 10% Nuclear 21% Hydro 2% When demand exceeds 95% of the daily Spinning - peak, 10% of the peak should be available reserve for spinning reserve 57.5 Table 1 presents some of the data used for the study. Column 2 represents the percentages of various generation types (column 1) in the energy mix. Columns 3 and 4 represent the capacity limits for various generation types, while the 5-th column represents the average cost of MWh produced by different generation types. The high cost of PV is still comparable with cost of some peaking gas turbine plants and does not take into account any subsidies

5 4. Results 4.1 Energy Savings without Contingencies PV systems can save energy, especially at peak load, which typically burns the most expensive fuel. Energy savings can directly be seen in Fig. 5, which indicates hourly unit allocation to minimize costs of generating electricity at the typical day of the year when the PV system is, or is not available. Since the demand exceeds daily peak at 1pm, spinning reserve without contingency is maintained in (a) and (b), amount of which is five percent of the full capacity. If the PV system produced power reliably, the PV system could save energy generated by gas turbines from the spinning reserve. Nuclear generation cannot decrease fast enough because of the very low up- and downramp ratio. Fig. 6 shows weekly allocation of generating plants for the same two scenarios. (a) Weekly generation profile without the PV system at 39th week (b) Weekly generation profile with the 10% PV system Fig. 6 Weekly generation profiles to minimize costs of generating electricity at the peak week of the year (a) Daily generation profile without the PV system at 274th day of the year (b) Daily generation profile with the 10% PV system Fig. 5 Daily generation profiles on a normal (274 th ) day of the year 4.2 Generation Costs of the Photovoltaic System [12, 14] This study examines costs of generating electricity of the renewable photovoltaic (PV) system. Solar PV is one of the most expensive renewable energy generation technologies. This study assumes generation costs of a solar PV system to be $/MWh (obtained as a levelized cost estimate of electricity produced by PV based on market prices for medium to large systems in 2010 and early 2011) in comparison to 45.3 $/MWh for coal-fired generation, 57.5 $/MWh gas-fired generation, and 6.60 $/MWh for nuclear generation. Fig. 7 shows the duration curves of normalized generation costs of all unit types and only gas-fired units. SR, No-SR, PV and No-PV indicates the case with the requirement of spinning reserve, without the spinning reserve, with the PV system, and without the PV system, respectively. Fig. 7 (a) shows total costs of all unit types. The blue line indicating No-SR and No-PV is below the red dotted line indicating No-SR and PV. Since generation cost of the PV system is more expensive than generation cost of the others, the PV system is not cost effective. Although the PV system is not cost effective on total costs of all unit types, it can be cost effective in comparison to the costs of gas turbines. Fig. 7 (b) indicates total costs of only gas-fired units which typically generate peak power, including spinning reserve. The PV system is decreasing the total costs when supplementing

6 gas-fired units in both cases of without and with the requirement of spinning reserve. That is, the PV system is cost effective. It is to be noted that the PV system prices have lately been changing so fast that it is very difficult to track the most recent levels (for example, monocrystalline Si cells reaching previously unheard of price levels close to $1.00/W and efficiencies of percent, which is percent lower than the prices from previous year). Current low prices are only partially due to the advances in manufacturing and developmental leaps. Much more, they are the result of a serious oversupply of PV cells and modules to a worldwide market still recovering from the economic recession in 2008 and suffering serious uncertainties about the economic growth opportunities in the near future while the problems are simultaneously affecting all of the world s major economies (which also happen to be the major manufacturers and consumers of PV technology). 5. Conclusion The aim of this study is to analyze the impact that significant presence of renewable energy generation, photovoltaic systems in this case, has on the costs of the grid. The chosen example is represented by a modified system of Georgia, with a hypothetical PV system portfolio added in the form of multiple small to medium scale systems amounting to 10 percent of the overall system peak load. Considering that it represents a total of nearly 4 GW p capacity while the cummulative capacity of the PV system additions in the USA amounted to some 2.6 GW p, the proposed scenario is a projection of what might become a viable planning option in several years, opening many questions, both on economic and engineering sides. It is to be noted that the issue of short term resolution and opertional uncertainty associated with renewables like PV and wind is not considered here. It requires the kind of scrutiny which is the subject of our ongoing work. Not yet being able to compete on cost with more conventional (and much cheaper) generation technologies, like fossil fuel driven and nuclear power plants, PV can still be viewed as a potentially attractive generation option. This study did not take into account any of the costs associated with emissions, nor impact of emissions on the cost of health care, or any regulatory impact that may in the future favor introduction of renewable generation into a generation mix. Consideration of such factors would bring the PV much closer to grid parity, which is not far. The growing costs of electric energy (which have increased by 50 percent over the last decade) are also making grid parity gap smaller. In addition to those intrinsic and external factors, utilization of PV as a substitute for expensive gas turbines in generation portfolio is an interesting perspective on the cost issue. (a) (b) Gas-fired units All unit types Fig. 7 Normalized duration curves of costs of generating electricity with the ten percent penetration of PV systems On the other side, the need for spinning reserve which is necessary to supplement the uncertain generation sources and the type of its deployment (which may force very strenuous deployment under some circumstances) may be the factor of cost increase which is yet to be fully accounted for and has long been a matter of heated discussions among researchers and system operators. 6. Acknowledgement The authors gratefully acknowledge support of National Science Foundation under grant # which was used for part of the work presented in this paper

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