ATC COMPUTATIONAL ISSUES

Transcription

1 ATC COMPUTATIONAL ISSUES Mark H. Gravener PJM Interconnection, L.L.C. Valley Forge, PA Chika Nwankpa Drexel University Philadelphia, PA Tai-Sim Yeoh Drexel University Philadelphia, PA Abstract A method of calculating Available Transfer Capability (ATC) and the exploration of the relative effects of certain computational issues are described in this paper. Specifically, the calculation of ATC is laid out for the purposes of pointing out the various computational aspects that affect it such as algorithmic tolerances and source/sink composition among others. Test cases from the Pennsylvania-Jersey-Maryland (PJM) Interconnection is used to obtain results on this study. Among the inferences obtained from this work is the necessity to properly account for uncertainties that exist not only in the physical structure of the power system but also those that exist in the computation of its properties reflected in ATC evaluation. In addition, from the studies on sink composition we notice from ATC values, underlying behavior that are characteristic of sub-areas within a given control area. The quantification of such effects can lead to a better understanding of the underlying properties involved in ATC computation. I. Introduction In 1992, the United States Congress developed the Federal Power Act, which has been interpreted by the Federal Energy Regulatory Commission (FERC) as a mandate to introduce open-access of transmission resources and generation competition to the electric power industry. From 1992 through the beginning of 1996, FERC issued a series of Notice of Proposed Rulemakings (NOPRs) that provided hints to the direction FERC was headed and sought industry comment. This process culminated in April of 1996 when FERC issued Order 888 (Promoting Utility Competition Through Open Access, Non-Discriminatory Transmission Service by Public Utilities; Recovery of Stranded Costs by Public Utilities and Transmitting Utilities) and 889 (Open Access Same-Time Information System and Standards of Conduct). Order 888 is intended to do much as its title suggests, while Order 889 mandated the calculation of an Available Transfer Capability (ATC) for each control area and the posting of these values on a communications system called the Open Access Same- Time Information System (OASIS). ATC is the limiting transfer value between two control areas (source and sink) that is available without any violation of power system operating properties, e.g. thermal overload and voltage limits. OASIS is a system that displays the ATC for a region and is accessible by market participants via public communications media such as the Internet. The purpose of calculating ATC and posting these values to an OASIS is to further the openaccess of the bulk transmission system by providing a market signal of the capability of a transmission system to deliver energy, which would spur competitive bidding in the generation, or energy, market. Development of technical guidelines for both ATC and OASIS has been deferred to the North American Electric Reliability Council (NERC), an industry group that develops reliability standards and guides for the planning and operation of electric power systems. NERC task forces have developed broad guidelines, and the regions that comprise NERC are currently interpreting the document and developing their own ATC process. The FERC mandate to calculate ATC poses a great problem to the electric industry. With these requirements, utility personnel on system and operations planning staffs are challenged with calculating ATC utilizing standard power flow solvers (e.g., PTI, GE, EPRI). Practical calculation methods must be developed that incorporate sound engineering principles to provide commercially viable transfer capability signals to the energy market. Understanding issues related to the computation of ATC can be critical to system planners, operators and market participants. For example, variations in tolerance values used as stopping criteria on search patterns for limiting contingencies will offer different ATC values. Of course, this information along with results from studies of varying the constituents of trading areas should go a long 1

2 way in improving the understanding power market behavior in terms of ATC values. In addition, a future contingency ranking scheme would be able to use this information since it also provides information on which equipment were overloaded and by how much. As expected, overload levels varied per algorithmic approach selected (not reported in this paper.) The calculated ATC should reflect the maximum control area to control area incremental transfer capability (modified to reflect various operating and planning margins) based on the ability of the interconnected transmission network to deliver energy. The network response method of deriving transfer capability [3,4] is espoused for this method, which acknowledges the nature of parallel flows on a highly networked system such as the Eastern Interconnection. II. Problem Formulation The ATC calculator described below enables transfers by increasing the complex load with uniform power factor at every load bus in the sink control area and increasing the injected real power at generator buses in the source control area in incremental steps until limits are incurred. Mathematically, this can be represented as the constrained non-linear optimization problem max λ s.t. f(x,λ) = f(x) - λb = 0 g(x,λ) 0 where λ is a scalar parameter representing the increase in bus load or generation, b is the bus load or generation, f(x,λ) is the set of augmented power flow equations, and g(x,λ) are the thermal and voltage constraints. The standard non-linear power flow equations are represented by where x=(v,θ). f(x) = [P(x)-P o, Q(x)-Q o ] = 0 III. ATC Calculator The ATC calculator developed utilizes a repetitive power flow method based on a generalized search method, where successive power flow solutions are conducted to establish the maximum transfer capability. Although this method can be time-consuming as compared to other methods still under development (such as the continuation power flow), the implementation reduces time to convergence on the maximum transfer capability. It avoids computationally expensive calculation of transfer step sizes which are found in continuation power flow techniques. The ATC calculator can be utilized to determine the nonsimultaneous real power transfer capability between any source-sink pair subject to the following constraints: Transmission line and transformer MW flows must be less than the appropriate MW rating Post-contingency voltage drop must be less than the specified value A combination of linear and non-linear analysis is used in this method. Both Newton and decoupled power flow solution methods are used to their best advantage, the fixed-slope decoupled solution method to initialize the solution of the non-linear power flow equations following large transfer steps and the Newton method to refine such solutions. Thermal contingency analysis utilizes a linear DC power flow and AC contingency analysis utilizes the fixed-slope decoupled solution method. The calculated ATC is the maximum increase in sink load that does not violate thermal or voltage criteria less margins that are applied. The increase in load is used as an indicator of incremental transfer capability via the increase in source generation due to a modified area interchange control that is utilized to prevent overloading of the swing machine. Swing machine output is monitored during the simulation, and when its output (increasing due to system losses) exceeds a user-defined tolerance, source area generation is increased to relieve the swing. Thus, the increase in source area generation reflects the energy dispatched to supply both sink area load and to compensate for losses. A generalized search algorithm is implemented to, first find the thermal limit of non-simultaneous transfers between two user-defined control areas. Violation of this criteria include pre-contingency overloading of branch normal ratings or post-contingency violation of branch emergency ratings. Once the thermal limit of transfers is determined, AC contingency checking is performed. If the power flow solution violates a voltage limit or does not converge, the generalized search algorithm is once again engaged to find the level of transfers that do not cause a violation of AC contingency criteria. Figure 1 provides a flow diagram of the ATC calculator. The most limiting result from either thermal or voltage limit-checking is the First Contingency Incremental Transfer Capability (FCITC). This value is then decreased by the appropriate margins, the result of which is ATC. The FCITC plus any same-direction base case transfers on the calculated path is the Total Transfer Capability (TTC), similar to the First Contingency Total Transfer Capability (FCTTC). Figure 2 illustrates the relationship between the application of margins and transfer capability for Firm ATC. 2

3 GENERATION DISPATCH SEARCH ALGORITHM TO MAXIMIZE SOURCE - SINK TRANSFERS NO SEARCH ALGORITHM TO FIND VOLTAGE LIMIT YES TRANSACTIONS BASE CASE CONDITIONS LINEAR ANALYSIS TRANSFER MAXIMIZED BASED ON THERMAL CRITERIA? YES AC ANALYSIS TOPOLOGY, LOADS DISTRIBUTION FACTORS SUBSYSTEM LIST CONTINGENCY LIST MONITORED LINE LIST another transfer step size is affected, and so on until a thermal violation is encountered. When this happens, the search flips direction from the last point (where violation is picked up) at halves the transfer step size. Following step sizes are always half the previous step sizes. If specific transfer causes a change in violation status, the next transfer changes direction. In Figure 3, regardless of whether or not a thermal limit is violated, when the next transfer step size is 125 MW, which is less than the convergence tolerance, the search stops. At this point, AC contingency checking is performed. If a voltage violation exists, the search algorithm will decrease transfers by the initial transfer step size, i.e. in our case 1000 MW. If no voltage violation had occurred, the ATC calculation would have been complete. Once again the search used in thermal limit identification will be used here for voltage limits. For this example, the First Contingency Incremental Transfer Capability is 3000 MW. VOLTAGE CRITERIA VIOLATION? NO Thermal Limit Search STOP MW Figure 1: ATC Calculator Flow Diagram IV. Generalized Search Algorithm Example An example of the generalized search algorithm is shown in Figure 3. For this example the user has selected the initial transfer step size during initiation of thermal or voltage limit searching to be 1000 MW. The user also has chosen a minimum step size of 200 MW that will stop the search during convergence to a thermal or voltage limit. Base case thermal pre- and post-contingency checking is performed, and if no violations occur a transfer of 1000 MW is affected by increasing source generation and increasing sink load. Power Flow Source Area to Sink Area (MW) Limit Reached Expected Conditions FIRM MARGIN CBM FIRM BASE CONDITION FCITC FIRM ATC Zero - Net FCTTC = TTC Same Direction Firm Base Transfers on Posted Path Figure 2: Relationship of Transfer Capability and Application of Margin for Firm ATC A full non-linear solution to allow controlling device movement prior to pre- and post-contingency checking is performed at every transfer step. If no violations occur, MW Voltage Limit Search Voltage Limit Thermal Limit Figure 3: Example of Generalized Search Algorithm In order to view the effects of tolerance effects on the resulting ATC values the program has been altered so as to incorporate changes in both the initial search (in transfers) step sizes as well as the convergence tolerance values. It will be shown that, dependent on the case, we notice a decreasing or increasing pattern to final limit. As shown in Figure 3, the thermal limit was reached in a decreasing pattern while the voltage limit was reached in an increasing pattern. V. Computational Issues Involved In ATC Calculation While we have introduced ATC calculation, another important focus of this paper lies in determining the effects of changing certain attributes of the calculation: Transfer step sizes in the search pattern Convergence tolerances Sink composition In our previous work [5], we exhibited the effects of change in external influences on ATC calculation. These influences included load forecast error and simultaneous transfer changes. It was found that additional information about the underlying transmission network can be 3

4 obtained from the sensitivity of ATC to these uncertainties. For example, an unexpected increase in ATC due to an increase in the load forecast error may suggest to the investigator that the underlying system possesses local generation that offsets transmission loading. In this section, we will show that a change in computational attributes listed above do affect ATC values. These represent a set of uncertainties exist which are internal as opposed to the external ones that were accounted for in [5]. A. Test System The Pennsylvania - New Jersey - Maryland Interconnection (PJM) is the largest control area in North America and consists of 10 electric utilities serving over 22 million people in a 48,700 square mile area. The region includes all of New Jersey, Delaware, the District of Columbia, major portions of Pennsylvania and Maryland, and a small portion of Virginia. PJM has an installed generating capacity of over 56,000 MW with a peak demand of approximately 50,000 MW. The region has 7,000 miles of EHV transmission lines. PJM has interconnections with the New York Power Pool, Virginia Power (VP), and various companies of the East Central Area Reliability Council (ECAR), specifically Allegheny Power (AP) and Cleveland Electric Illuminating (CEI). PJM is represented at NERC by the Mid-Atlantic Area Council (MAAC), whose borders are contiguous with PJM. The PJM system operator directs all bulk power system operations, including the dispatch of generation, control of transmission, administration of transmission services, grid accounting, and the functions mandated by FERC Order 889 such as the development and maintenance of an OASIS and the calculation of ATC. The specific case investigated in this paper is a 1997 Summer Intermediate Load Case for the PJM system with an approximate value of 2,600 MW of net imports. Sensitivity analysis was conducted on the ATC of a commercially viable path from ECAR into PJM with respect to the following three changes: Transfer step sizes in the search pattern, Convergence tolerances and Sink composition (Figure 4). B. Transfer Step Sizes and Convergence Tolerances Shown in the graph below is the effect of changing the transfer step changes in the algorithm from 200 to 600 to 1000 MW values. In order to appreciate what is occurring in these plots one should refer back to Figure 2 that outlines the search algorithm. First of all not all plots reflect a qualitatively similar decreasing/increasing behavior with increase in convergence tolerance. As previously mentioned in Section IV, this is dependent on whether or not limit (thermal) is reached in either a decreasing or increasing pattern. In the former case, one ECAR MECS AEP CEI OH AP NPCC VP SERC NYPP PJM NEPOOL MAAC Figure 4: General Interconnection Diagram and Associated NERC Regions Plot of ATC vs Convergence Tolerence For Whole PJM Control Area MW 3.03 % MW 4.51 % MW 3.88 % Convergence Tolerence (MW) Figure 5. Results of Runs Describing the Effects of Convergence Tolerances and Transfer Step Sizes of 200, 600, 1000 MW on ATC for the Whole PJM Control Area would expect to see an increase in ATC values with increase in convergence tolerance. This is shown in the cases of transfer step sizes of 200 MW and 600 MW. The reverse case occurs for step size of 1000 MW. It should be noted that this does not always occur, i.e. either monotonously decreasing/increasing behavior, because oscillations may occur during convergence to the estimated limit. Deviations in percentage from mean ATC values for the various step sizes are also provided in Figure 5. C. Sink Composition Figure 6 above shows the map of the PJM operating territory. There are 10 investor owned utility companies that make up the physical backbone of the region. 4

5 Plot of ATC vs Convergence Tolerence For PJM - North East (Load Areas 1,5) MW 8.11 % 600 MW 7.41 % 1000 MW % Convergence Tolerence (MW) Figure 7. Results of Runs Describing the Effects of Convergence Tolerances and Transfer Step Sizes on ATC for PJM Northeast Area Plot of ATC vs Convergence Tolerence For PJM East Areas 1,2,5,9,10) (Load MW 5.88 % 600 MW 8.68 % 1000 MW 8.03 % Figure 6. Map of Whole PJM Control Area with Associated Utility Companies Generally, ATC is evaluated by looking at only area to area transfers. In the case of PJM this means the lumping together of the ten companies to form the sink in our calculations. That is exactly what was done in [5] and in the above-mentioned analysis of algorithmic effects. Now we will show results of changing the composition of the sink to three other cases, which we will call (Figures 7-9): PJM Northeast Companies 1 and 5 PJM East Companies 1, 2, 5, 9 and 10 PJM South Companies 4 and 8 In other words, instead of raising the corresponding loading of all 10 contributing companies during a given transfer step, we just increased the loading of the listed sub-areas. Information obtained from this study should lead to an understanding of sensitivities of sub-areas of PJM to the overall ATC value. Also provided are the percent deviation values from their means as way of providing a scale on the uncertainties involved in this calculation. As expected, in each of the sub-area cases, the deviations increased in comparison to the whole control area investigations shown in Figure 5. Figure 8. Results of Runs Describing the Effects of Convergence Tolerances and Transfer Step Sizes on ATC for PJM East Area Convergence Tolerence (MW) Plot of ATC vs Convergence Tolerence For PJM South Areas 4,8) (Load 600 MW 4.65 % MW 3.77 % Connvergence Tolerence (MW) 200 MW 4.47 % Figure 9. Results of Runs Describing the Effects of Convergence Tolerances and Transfer Step Sizes on ATC for PJM South Area VI. Conclusion A method of calculating ATC and quantifying the effects of algorithmic changes such as transfer step sizes and convergence tolerances on ATC is presented in this paper. This paper also exhibits the effects of sink composition on ATC calculation (under varying algorithmic conditions). Additional sensitivity information can be derived from the plots that are 5

6 characteristic of the specific sub-area being studied. In addition, a future contingency ranking scheme would be able to use this information since it also provides information on which equipment were overloaded and by how much. The ATC calculator incorporates both linear and nonlinear analysis, which is essential to capture the phenomena of steady-state AC power systems. The nonlinear ATC calculations are time intensive but necessary, and systems that have multiple interconnections can find themselves unable to calculate path ATCs as often as they would prefer. Because of this, the appropriate selection of final convergence tolerances should not only be chosen to fulfil speed of ATC evaluation but also incorporate the intrinsic uncertainty information it represents. Results showed that when transfer step sizes were varied, ATC values varied by as much as 8%. This has enormous economic impact. The same can be said about the effects of changing the composition of sinks on the ATC. With this in mind future work should concentrate on improving search algorithms for ATC evaluation while maintaining computational efficiency. VIII. References [1] Promoting Utility Competition Through Open Access, Non-Discriminatory Transmission Service By Public Utilities; Recovery Of Stranded Costs By Public Utilities And Transmitting Utilities, Order No. 888, Final Rule, FERC, April 24, [2] Open Access Same-Time Information System And Standards Of Conduct, Order No. 889, Final Rule, FERC, April 24, [3] Available Transfer Capability Definitions and Determination, A Framework for Determining Available Transfer Capabilities of the Interconnected Transmission Networks for a Commercially Viable Electricity Market, North American Electric Reliability Council, June [4] Transmission Transfer Capability, A Reference Document for Calculating and Reporting the Electric Power Transfer Capability of Interconnected Systems, North American Electric Reliability Council, May [5] Gravener, M. and Nwankpa, C. O., Available Transfer Capability And First Order Sensitivity, Presented at the 1998 PES Summer Meeting, San Diego, CA. July 13-16,