Siemens Energy, Inc. Power Technology
Issue 107
Automatic Generation Control (AGC) Dynamic Simulation in PSS®E Lu Wang, Ph.D. Staff Software Engineer Siemens PTI
[email protected]
Dingguo Chen, Ph.D. Staff Engineer Siemens E D EA
[email protected]
Introduction Climate change and environmental concerns are tremendously influencing and shaping the future of the power industry. As a positive consequence, there has been a remarkable, rapid increase in the past several years in the megawatts produced by renewable energy resources across the globe, and this trend will continue for the next decades. These renewable energy resources, including wind generating units and solar generation, are for the most part intermittent in nature. Smart Grid technologies will enable power systems to operate with larger amounts of these energy resources since they enable both the suppliers and consumers to compensate for such intermittency. New features addressing the intermittent nature of these resources should be added into Energy Management Systems (EMS) and power system planning, so that systems with Smart Grids can be operated safely. Automatic Generation Control (AGC) is an important function in modern EMS systems. Since January 1998, new control performance standards (CPS) have been enforced in North America by the North American Electric Reliability Corporation (NERC). NERC requires that control areas must be no less than 100% compliant with CPS1 and no less than 90% compliant with CPS2. CPS1 measures the correlation of a control area’s area control error (ACE) and interconnection frequency error over a moving window of a 12-month duration. CPS2 measures how many times a control area manages to hold the magnitude of its 10-minute ACE average within a predetermined ACE limit over a calendar month duration. In addition to the new CPS criteria, the new disturbance control standard (DCS) was proposed to ensure that the balancing authority is able to utilize its contingency reserve to balance resources and demand and return interconnection frequency within defined limits following a reportable disturbance. These control performance criteria continue to evolve. Adjustments to these control performance criteria have been made over time, for instance, with the inclusion of automatic time error correction. The increased number of renewable energy resources connected into power grids definitely imposes great challenges on AGC. Questions arise which need to be answered: Can the current AGC in EMS meet the NERC criteria? How much power injection from renewable energy resources can be connected so that NERC criteria can still be met? If a new wind farm is planned, can it be connected to power grids without violating NERC criteria on AGC? PSS®E can answer these questions. PSS®E provides the capability to simulate extended term dynamics in power systems. The simulation may extend to an unlimited period and include the effects of slow acting controls and equipment, such as AGC, switched shunts, load tap changing transformers, load changes, etc. The integration time step may vary in the course of the simulation. Theoretically, there is no upper limit for the integration time step and it can be very large (e.g., 0.2 seconds). This article first describes extended term dynamic simulation in PSS®E. Then three user-written models are developed for extended term dynamic simulation, namely an AGC model, a load model and a wind generation model. Simulation is run on a small power system. Simulation results are presented and explained. Conclusions are made. The simulation presented in this article can quantify AGC performance. It can be used for validating AGC performance both in EMS for real-time operation and in power system planning for future renewable energy resource connections.
Power Technology
February 2011
Extended Term Dynamic Simulation [1] Extended term dynamic simulation in PSS®E is implemented using implicit (trapezoidal) integration. When compared with the state space dynamic simulation in PSS®E which is implemented using improved Euler’s method, extended term dynamic simulation has advantages: it allows a large integration time step (theoretically, there is no upper limit for the integration time step) for quicker simulation, allows the integration time step to change in the course of simulation and assures numerical integration stability at the same time. PSS®E was initially designed to model transients over a period of few cycles to several seconds following disturbances. During this time frame, the important effects are inertial motions of turbine generators as affected by the characteristics of generators, excitation systems, loads, static var sources, DC converters and, to a lesser extent, turbine-governors. These phenomena have been broadly labeled Power System Stability by power system engineers. The bandwidth of the effects being modeled is limited to about 10 Hz at the high end with typical integration time steps of 0.00833 seconds (1/2 cycle) for 60-Hz systems and 0.01 seconds (1/2 cycle) for 50-Hz systems. Higher frequency effects require modeling of the electrical network with differential equations using much smaller time steps, the domain of electromagnetic transients programs. At the low-frequency end, the dynamic system models being represented are valid down to 0 Hz or steady state. Thus within the bounds of modeling assumptions (loads modeled without allowance for longer term constant power control effects, no tap changer action in substation transformers, no switching of reactive sources, and no AGC or boiler effects) the dynamic simulation is valid within a time scale resolution of about 20 ms to infinity. As the time spectrum of power system dynamic effects is extended beyond several seconds, additional effects come into play, such as the tendency of loads to exhibit constant power characteristics through tap changer and/or load control devices, automatic switching of reactors or shunt capacitors, prime mover power changes through primary speed control and/or AGC. Simulation of such longer-term effects requires additional modeling of load restoration mechanisms and prime mover characteristics including boiler effects, exhaust temperature control effects on gas turbines, etc. Extended term simulation has three modes of operation, selected automatically and based on the size of the time step and user-defined thresholds: For small time steps, such as the typical one-half cycle time step, the simulation response will be essentially identical to that of simulations using the state space method. For larger time steps, typically 0.05 to 0.1 seconds (3 to 6 cycles for a 60-Hz system), all states of the model and, hence, all swing modes are preserved. Damping of the lower frequency swing modes is preserved while higher frequency swing modes tend to be filtered out. Numerical stability is maintained. For even larger time steps, 0.15 to 0.2 seconds, the program switches to a mode where the rotor angle of each generator is adjusted at each time step to yield electrical torque equal to mechanical torque less the unit’s share of the connected system’s global accelerating torque. This mode may be used when all units in an island follow essentially the same frequency. At the user’s discretion, the time step can be changed at any point in the simulation to adjust the solution mode, i.e., to disclose high-frequency characteristics for a few seconds following a disturbance and then revert back to a large time-step mode. If modeling results in an island with generators all essentially infinite (very large inertias, H), then the constant island frequency mode should not be used. This mode assumes all units are at the same speed. With infinite inertias, all machines, by default, are at the same frequency (speed). To increase the time step, the user should also increase the constant island frequency threshold, DLTEXT. It is natural to expect that, with the increased integration step, details of “fast” processes will be lost. The user should always keep a balance between the level of accuracy and the duration of the simulation. Most of the standard models distributed with PSS®E can be used for the extended term simulation and user-written models are allowed in the extended term simulation. These models which have “state” variables and calculate derivatives must follow additional procedures established for extended simulation models. All user-written models must follow the additional procedures to be used in extended term simulations. Page 2
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User-written AGC Model The AGC control logic consists of two levels of control mechanisms: control area level and generating unit level. On the control area level, the ACE equation is utilized to calculate ACE, which includes two major components, ACE frequency component due to frequency deviation from its nominal value, and ACE interchange component due to actual net interchange deviation from its scheduled net interchange value. Additional ACE components may be incorporated as necessary, which may include time error correction, meter error, ACE offset, etc. Once ACE is calculated, the control area’s total desired generation (PTDG) may be derived based on a proportional-integral-derivative (PID) control scheme or based on the statistics of running CPS1 and CPS2 and the user-desired CPS1 and CPS2 targets. On the generating unit level, the control area’s PTDG is allocated to each participating generating unit per economic consideration, response speed, reservation contribution, unit’s operating mode, and unit’s characteristics. This article considers a single area AGC control logic and therefore does not deal with anything but the frequency component of ACE. A simple AGC model is built that controls the system frequency for the conditions when the load in the system follows the given load demand and there is an intermittent component of the wind generation. To facilitate the simulation of AGC, three major steps are involved: Determine the control area's total desired generation. Determine the AGC unit's base points. Determine the AGC unit's regulation obligation. A. Determine the control area's total desired generation While there may be more ACE components to be considered in the ACE equation, the single-area simulation here is limited to include only the one most important ACE component: ACE frequency component. The ACE is calculated as follows:
ACE 10 Bf where B is the frequency bias in units of MW/0.1Hz, and Δf is the frequency deviation in Hz. The AGC PID control logic is shown in Fig. 1.
GP
ACE
GI s
Σ
PTDG
GD s 1 sTD Figure 1 - AGC Control Logic It should be pointed out that the state variables in the AGC PID controller are integrated differently than other PSS®E state variables (e.g., the ones in generator models) during simulation. The AGC PID integration time step is generally AGC cycle interval (e.g., 4 seconds or 2 seconds) while the integration time step in PSS®E extended term simulation ranges from 0.00833 to 1 second. The PID integrator state variable is initialized so that the integrator output is the initial total generation, that is, PTDG equals the total Page 3
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February 2011
generation when ACE=0. During simulation, the integrator is reinitialized so that its output equals the current total generation whenever ACE changes across zero (when ACE changes sign). B. Determine the AGC unit's base points The unit desired generation for each participating AGC unit is split into two components: the base point and the regulation. The base point of each AGC participating unit is set at its Economic Dispatch (ED) point: Pbpi = PEdi where PEDi is calculated mathematically by an ED program, Pbpi is the base point. C. Determine the AGC unit's regulation obligation With step A to determine the control area's total desired generation, and with step B to determine AGC unit's base points, the control area's total regulation is calculated as the difference between the control area's total desired generation and the sum of the AGC unit's base points: PRegsys = PTDG - ΣPbpi where PRegsys is the control area’s total regulation. The control area's total regulation is then allocated among all regulating units. There are various kinds of regulation allocation schemes. A simple regulation allocation scheme is proposed and used in the simulation: PRegi = min{(RRi / Σ RRj) PRegsys, PRegmaxi - Pbpi} where PRegi is the regulation obligation of unit i, RRi is the ramp rate of unit i, and PRegmaxi is the maximum regulation for unit i. The unit's regulation is allocated based on unit's ramp rate share and subject to its maximum regulation with the unit's base point set to Pbpi. If any unit's desired regulation PRegi plus its base point hits its maximum regulating limit, then subtract the regulation allocated to this unit from the area's total regulation, then allocate the remaining area's total regulation among the remaining regulating units. User-written Load Model A simple load model is used for all loads in the system to be simulated. Loads vary in time. System load forecast and distribution factors are used to calculate loads at buses. It is assumed that each load has constant power factor. The load model used in this article is shown in Fig. 2.
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Psystem(t)
Σ
Dil
δ(t)
1 K pfil f i (t )
Pil(t)
Δfi(t)
1 1 Pf il2
1 K qfil f i (t )
Qil(t)
Figure 2 - Load Model where Psystem(t) is system load forecast, δ(t) is the load disturbance, Dil is the load distribution factor at bus i, Δfi(t) is the frequency deviation at bus i, Kpfil and Kqfil are the active and reactive load frequency sensitivities respectively at bus i, Pfil is the load power factor at bus i. Pil(t) and Qil(t) are split into three parts: constant MVA load, constant I load and constant Y load, which are used to calculate the current injection at bus I according to the voltage at bus i. User-written Wind Generation Model The wind generation is modeled as a generator with time varying active power output and constant power factor. The active power output is intermittent. The typical data can be obtained from an actual wind farm. The wind generation model is shown in Fig. 3.
Piwg(t)
Piwg(t)
1 1 2 Pf iwg
Qiwg(t)
Figure 3 - Wind Generation Model where Piwg(t) is the wind generation active power output, Pfiwg is the constant wind generation power factor at bus i, Piwg(t) and Qiwg(t) are the actual MW and Mvar of the wind generation at bus i. System for Simulation A 23-bus system is used for simulation. The system is shown in Fig. 4.
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Figure 4 - A 23-bus System This is a single area system. There are five regular generation units and a wind generation unit in the system. Each of the five regular generation units has a generator model, exciter model, and governor model. The wind generation unit is connected to bus 3018. It is dispatched at 100 MW with the given power factor. Four of the five regular generation units are AGC controlled (regulating units). AGC control cycle interval is 4 seconds. This system initially has about 3200 MW load. Some tentative data are used for the load forecast and wind generation. The system load forecast is shown in Fig. 5. It is a sine wave deviating from 3200 MW to 1600 MW with a cycle of 3600 seconds. The wind generation data is shown in Fig. 6. Both are in pu of 100 MVA. The wind generation is also a sine wave with the magnitude of 50 MW and a cycle of 180 seconds.
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Figure 5 - System Load Forecast (in pu of 100 MVA)
Figure 6 - Wind Generation (in pu of 100 MVA) Page 7
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Simulation Results The extended term simulation is run for a 3 hour period using PSS®E. The simulation results are shown in Fig. 7 – Fig. 12. Fig. 7 shows the frequency deviation. Due to AGC, the frequency is kept in a very narrow range not exceeding 0.15%. Fig. 8 shows the ACE. It can be seen that the frequency deviation and ACE have similar shape but in opposite sign due to the fact that the system simulated is a single area. Fig. 9 shows the total desired generation. The spikes are caused by the re-initialization of AGC PID controller. Fig. 10 shows the total generation. It can be seen that both the total desired generation and the total generation respond well with the load change and wind generation change. Fig. 11 shows CPS1 and Fig. 12 shows CPS2. Both are compliant with NERC standards (CPS1>100%, CPS2>90%).
Figure 7 - System Frequency Response (frequency deviation in pu of 60 Hz)
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Figure 8 - ACE (MW)
Figure 9 - Total Desired Generation (MW) Page 9
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Figure 10 - Total Generation (pu of 100 MVA)
Figure 11 - CPS1 (%) Page 10
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Figure 12 - CPS2 (%) Conclusions With more and more renewable energy resources connected into power grids, their impacts on AGC must be understood both at the planning stage and in real time operation. PSS®E provides customers with the capability to simulate AGC dynamically under the condition of intermittent generation and varying load. This simulation can help the power system planner to study and understand AGC behavior when a renewable energy resource is planned. As long as the current operating plan and other necessary information are available, system operators can use PSS®E’s AGC dynamic simulation capability to determine if NERC AGC control criteria are met. This article described an example of the simplified AGC PSS®E model applied to the single area sample system using PSS®E. The results of the simulation showed how AGC can positively affect the frequency of the system when the loads of the system follow the given forecast and there is an intermittent component in generation. Acknowledgement The authors would like to thank Dr. Yuriy Kazachkov for his review, comments and suggestions. Reference: [1] Siemens PTI, PSS®E 32 Program Application Guide, 2009.
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