Shanghai University of Electric Power Entrance Exam Set

The question probes the understanding of power system stability, specifically transient stability, which is crucial for the Shanghai University of Electric Power’s curriculum. Transient stability refers to the ability of a power system to maintain synchronism when subjected to a large disturbance, such as a fault. The critical clearing time (CCT) is the maximum time a fault can persist before the system loses synchronism. Beyond this time, the kinetic energy accumulated by the generator rotor due to the fault-induced imbalance between mechanical and electrical power will cause it to accelerate uncontrollably, leading to instability. The concept of the equal-area criterion is a fundamental method for estimating the CCT. It involves analyzing the swing equation, which describes the rotor angle dynamics. The area under the power-angle curve representing the excess kinetic energy during the fault is compared to the area representing the restoring electrical power after the fault is cleared. The CCT is the time at which these two areas are equal. Therefore, understanding the physical meaning of the swing equation and the graphical interpretation of the equal-area criterion is paramount. The ability to relate the severity of a disturbance (fault type and location) and the system’s response (post-fault power transfer capability) to the CCT is a core competency for power system engineers. A longer CCT indicates a more robust system against transient disturbances.

The question probes the understanding of distributed generation integration challenges within a power grid, specifically focusing on the impact of intermittent renewable sources on grid stability and operational efficiency. The Shanghai University of Electric Power Entrance Exam often emphasizes practical applications of electrical engineering principles in modern grid contexts. The core issue is how to manage the variability of sources like solar and wind power without compromising grid reliability. This involves considering factors such as voltage fluctuations, frequency deviations, and the need for ancillary services. When integrating a significant percentage of distributed renewable energy sources (DRES) into a traditional power grid, the primary challenge is maintaining grid stability and power quality due to the inherent intermittency and variability of these sources. Unlike conventional synchronous generators, DRES, particularly those based on power electronics (like solar PV and wind turbines), do not inherently provide inertia to the grid. This lack of inertia makes the grid more susceptible to rapid frequency deviations following disturbances, such as the sudden loss of a large conventional generator or a significant change in load. Furthermore, the bidirectional power flow introduced by DRES can complicate voltage control and protection schemes. Without proper management, voltage can fluctuate beyond acceptable limits, leading to equipment damage and power quality issues. The reactive power compensation strategies employed by conventional generators are often different from those of DRES, requiring advanced control systems to ensure voltage stability. The need for accurate forecasting of renewable energy generation is paramount. Forecast errors can lead to mismatches between supply and demand, necessitating rapid adjustments from dispatchable generation sources or energy storage systems. This also impacts the economic dispatch of power, as the cost of managing variability must be factored in. Therefore, the most critical aspect for advanced students to understand is the multifaceted impact of DRES on grid inertia, frequency regulation, voltage control, and the necessity for sophisticated forecasting and control mechanisms to ensure a stable and reliable power supply. This encompasses understanding the role of smart grid technologies, energy storage, and advanced grid management systems in mitigating these challenges.

The question probes the understanding of power system stability, specifically transient stability, in the context of a sudden load increase. Transient stability refers to the ability of a power system to remain synchronized after a large disturbance, such as a fault or a sudden change in load or generation. The critical clearing time (CCT) is the maximum duration a fault can persist before the system loses synchronism. However, this question is not about fault clearing but about the system’s response to a load change. When a sudden load increase occurs in a power system, generators connected to the grid will experience a decrease in their mechanical power input relative to their electrical output (assuming governor response is not instantaneous). This imbalance causes the rotor angle of the affected generators to decelerate relative to the synchronous speed. The system’s ability to recover from this disturbance depends on the inertia of the rotating masses, the strength of the interconnections, and the damping characteristics of the system. A sudden, significant increase in load without a corresponding immediate increase in generation will lead to a drop in system frequency and a deceleration of generator rotors. If this deceleration is too large, or if the system cannot adequately compensate through governor action and other control mechanisms, generators can lose synchronism with the rest of the system. The concept of “swing equation” is fundamental here, describing the rotor dynamics. The system’s ability to maintain synchronism after a load perturbation is directly related to the energy stored in the rotating masses and the rate at which this energy can be redistributed or absorbed. A more robust system, characterized by higher inertia, stronger interconnections, and effective damping, will be more resilient to such disturbances. The question asks about the most critical factor for maintaining synchronism following a sudden load increase. While load shedding can be a remedial action, it’s a response to instability, not a primary factor in preventing it from the generator’s perspective. Generator excitation control primarily affects voltage stability and reactive power, not directly the mechanical-electrical power balance causing rotor angle deviations in transient stability scenarios. The speed governor’s role is crucial in adjusting mechanical input to match electrical output, but its effectiveness is limited by its response time and the magnitude of the load change. The inherent inertia of the rotating masses provides a buffer against rapid changes in speed, allowing control systems more time to react. Therefore, the kinetic energy stored in the rotating machinery, which is directly proportional to inertia, is the most fundamental property that resists changes in rotor speed and thus helps maintain synchronism during sudden load variations.

The question probes the understanding of power system stability, specifically transient stability, which is a critical area of study at Shanghai University of Electric Power. Transient stability refers to the ability of a power system to maintain synchronism when subjected to a large disturbance, such as a short circuit. The critical clearing time (CCT) is the maximum time a fault can persist before the system loses synchronism. For a synchronous generator connected to an infinite bus through a network, the swing equation describes the rotor dynamics. The area under the power-angle curve during the fault and post-fault conditions is crucial for determining stability. The energy function method, particularly the Lyapunov’s direct method, provides a way to assess stability without solving the differential equations directly. The concept of the “equal-area criterion” is a graphical method derived from the energy function concept for a single-machine infinite-bus system. It states that if the area under the accelerating power curve (power deficit) during the fault is less than or equal to the area under the decelerating power curve (power surplus) after the fault is cleared, the system remains stable. In the context of the question, the system is initially operating at a stable equilibrium point. A fault occurs, causing a sudden drop in the electrical power output, leading to acceleration of the rotor. The clearing of the fault restores a higher level of electrical power. Stability is maintained if the kinetic energy gained by the rotor during acceleration (represented by the first area) can be dissipated by the decelerating power after the fault is cleared (represented by the second area). The critical clearing time is the time at which these two areas are exactly equal. Therefore, the ability to maintain synchronism is directly related to the system’s capacity to absorb the kinetic energy imparted to the rotor during the disturbance, which is fundamentally governed by the energy balance represented by the equal-area criterion. This criterion is a cornerstone for understanding the transient behavior of power systems and is extensively covered in power system stability courses at institutions like Shanghai University of Electric Power, emphasizing the importance of rapid fault clearing.

The question probes the understanding of the fundamental principles of power system stability, specifically transient stability, in the context of a synchronous generator connected to an infinite bus. The scenario describes a fault occurring at a specific location and its subsequent clearance. The core concept being tested is how the clearing time of a fault impacts the rotor angle dynamics of the generator and its ability to remain synchronized. The critical clearing time (CCT) is the maximum fault duration for which the system can recover and maintain synchronism. If the fault is cleared within the CCT, the generator’s kinetic energy, which initially increases due to the fault-induced power deficit, can be dissipated through the generator’s mechanical input and electrical output, allowing the rotor angle to oscillate and eventually settle. If the fault persists beyond the CCT, the accumulated kinetic energy will cause the rotor angle to increase beyond the point of no return (typically \( \pi \) radians or 180 degrees relative to the infinite bus), leading to loss of synchronism. In this scenario, the fault is cleared at \( t = 0.15 \) seconds. The question implies that this clearing time is *after* the critical clearing time. This means that even with the fault removed, the generator has already accumulated enough angular momentum to cause it to fall out of step with the infinite bus. The system’s ability to recover is compromised because the fault duration exceeded the threshold for transient stability. Therefore, the generator will lose synchronism. The explanation of why this happens involves the swing equation, which describes the rotor dynamics. During the fault, the electrical power output is significantly reduced, while the mechanical power input remains constant (assuming instantaneous mechanical torque response). This imbalance leads to an acceleration of the rotor. The area under the power-angle curve represents the change in kinetic energy. If the fault is cleared after the CCT, the area representing the accelerating energy (area between mechanical power and electrical power during the fault) exceeds the area representing the decelerating energy (area between electrical power and mechanical power after fault clearance) up to the point where the rotor angle reaches \( \pi \) radians. This fundamental principle dictates that the system will become unstable.

The question probes the understanding of the fundamental principles governing the integration of renewable energy sources into a national grid, specifically focusing on the challenges and solutions relevant to advanced power systems engineering as taught at Shanghai University of Electric Power. The core concept here is grid stability and the management of intermittency. When a significant percentage of a power grid relies on variable renewable energy (VRE) sources like solar and wind, the grid operator must ensure that the supply of electricity consistently matches demand in real-time, while also maintaining critical parameters like frequency and voltage within acceptable limits. The primary challenge posed by VRE is their inherent variability and unpredictability. Unlike conventional synchronous generators that inherently provide inertia and contribute to grid stiffness, VRE sources like photovoltaics and wind turbines often connect through power electronic inverters. These inverters, while efficient, may not inherently provide the same level of inertial response or fault ride-through capabilities as traditional generators. This can lead to faster frequency deviations during disturbances and increased susceptibility to voltage instability. To mitigate these issues, advanced grid management techniques are employed. Energy storage systems (ESS), such as batteries, pumped hydro, or compressed air energy storage, are crucial for smoothing out VRE output, absorbing excess energy during periods of high generation and low demand, and releasing stored energy during periods of low generation and high demand. This helps to balance supply and demand and reduce the impact of VRE intermittency. Furthermore, sophisticated forecasting techniques are essential to predict VRE output with greater accuracy, allowing grid operators to schedule conventional generation or dispatchable resources more effectively. Demand-side management (DSM) and flexible load control can also play a significant role by adjusting consumption patterns to align with VRE availability. Advanced control strategies for inverters, often referred to as “grid-forming” capabilities, are also being developed to enable VRE to actively support grid stability by providing synthetic inertia and voltage regulation. Considering these factors, the most comprehensive and effective approach to integrating a high penetration of VRE into a robust power system, as would be emphasized in the curriculum at Shanghai University of Electric Power, involves a multi-faceted strategy. This strategy must address the variability through storage, improve predictability through forecasting, enhance grid flexibility through demand-side measures, and leverage advanced inverter controls. Therefore, a combination of energy storage deployment, enhanced forecasting accuracy, and the implementation of advanced grid-forming inverter controls represents the most robust solution.

The question probes the understanding of grid synchronization principles, specifically focusing on the critical parameters for connecting a distributed generation (DG) system to the main power grid, as is a core competency for students at Shanghai University of Electric Power. The scenario describes a synchronous generator intended for integration. For successful synchronization, several conditions must be met to avoid damaging transients and ensure stable power flow. These conditions are: voltage magnitude equality, frequency equality, and phase angle equality. While phase sequence is also crucial for three-phase systems, the question specifically asks about the *immediate* pre-connection checks that are most critical for preventing operational issues. Voltage magnitude ensures that the DG unit does not cause significant voltage fluctuations upon connection. Frequency matching prevents the induction of large currents due to frequency differences. Phase angle matching ensures that the instantaneous voltage waveforms are aligned at the point of connection, minimizing inrush currents and mechanical stress. The concept of power factor, while important for overall grid operation and efficiency, is a consequence of the connection and the DG unit’s control strategy, not a prerequisite for the *act* of synchronization itself. Therefore, voltage, frequency, and phase angle are the primary synchronization parameters.

The question probes the understanding of grid stability and the impact of distributed energy resources (DERs) on power system inertia. Inertia in a power system is the tendency of rotating masses (primarily synchronous generators) to resist changes in frequency. When a disturbance occurs, such as a sudden load increase or generator outage, the kinetic energy stored in these rotating masses helps to maintain system frequency. The rate of change of frequency (RoCoF) is a critical metric for grid stability, indicating how quickly frequency deviates from its nominal value. Modern power grids are increasingly incorporating inverter-based resources (IBRs) like solar photovoltaics and wind turbines. Unlike synchronous generators, most IBRs do not inherently provide rotational inertia. While advanced control strategies can enable IBRs to emulate inertia (synthetic inertia), their response characteristics and effectiveness can differ from traditional synchronous machines. A significant penetration of IBRs without adequate inertia support can lead to higher RoCoF, making the system more vulnerable to frequency excursions and potentially leading to instability or cascading failures. Therefore, to maintain grid stability and manage RoCoF effectively in a system with high DER penetration, strategies that enhance or supplement inertia are crucial. These include: 1. **Maintaining a minimum level of synchronous generation:** Keeping a certain capacity of traditional synchronous generators online, even if not fully dispatched, to provide inherent inertia. 2. **Deploying grid-forming inverters:** These inverters can actively control voltage and frequency, mimicking the behavior of synchronous machines and contributing to system inertia. 3. **Utilizing fast-acting energy storage systems:** Battery energy storage systems (BESS) can rapidly inject or absorb power, effectively providing inertia-like response through their control systems. 4. **Implementing advanced frequency control schemes:** These schemes coordinate the response of various resources, including IBRs with synthetic inertia capabilities and controllable loads, to manage frequency deviations. Considering the context of Shanghai University of Electric Power’s focus on power system engineering and smart grids, understanding these advanced concepts is paramount. The question aims to assess a candidate’s grasp of how the evolving generation mix impacts fundamental grid stability principles and the innovative solutions required to address these challenges. The correct answer focuses on the proactive measures needed to counteract the inertia reduction caused by DERs, specifically highlighting the role of grid-forming capabilities and energy storage as key enablers of future grid stability.

The question probes the understanding of the fundamental principles governing the operation of synchronous generators, specifically focusing on the impact of excitation current on their performance characteristics. A synchronous generator, when operating in parallel with the grid, can function as either an over-excited generator (supplying reactive power, lagging power factor) or an under-excited generator (absorbing reactive power, leading power factor). The excitation current directly controls the magnetic field strength within the generator. Increasing the excitation current strengthens the magnetic field, leading to a higher generated electromotive force (EMF). When a synchronous generator is connected to an infinite bus (representing the power grid), its terminal voltage is essentially fixed. The real power output (\(P\)) is primarily determined by the mechanical input power and the difference in phase angle between the generated EMF and the terminal voltage. The reactive power output (\(Q\)) is significantly influenced by the excitation current. Consider a synchronous generator operating at a constant real power output. If the excitation current is increased (over-excitation), the generated EMF (\(E\)) increases. To maintain the same real power output with a higher EMF, the phase angle difference (\(\delta\)) between \(E\) and the terminal voltage (\(V\)) must decrease. The reactive power output is given by \(Q = \frac{|E||V|}{X_s} \sin(\delta)\), where \(X_s\) is the synchronous reactance. As \(|E|\) increases and \(\delta\) decreases, the term \(\frac{|E|}{X_s} \sin(\delta)\) can increase or decrease depending on the initial operating point. However, a more direct relationship exists: increasing excitation current increases the internal EMF, which, for a fixed real power output and terminal voltage, forces the generator to supply more reactive power to the grid. Conversely, decreasing excitation current (under-excitation) reduces the internal EMF, causing the generator to absorb reactive power. Therefore, to operate a synchronous generator at a leading power factor, it must be over-excited, meaning its excitation current is higher than that required for unity power factor operation at the same real power output. This over-excitation leads to the generator supplying reactive power to the grid. The Shanghai University of Electric Power Entrance Exam emphasizes the practical application of these principles in power system stability and control, making the understanding of excitation control crucial for future engineers.

The question probes the understanding of the fundamental principles of power system stability, specifically focusing on transient stability and the role of generator inertia. Transient stability refers to the ability of a synchronous machine to remain in synchronism with the rest of the power system following a disturbance. The critical clearing time (CCT) is the maximum time a fault can persist before the system loses synchronism. The swing equation, \( \frac{d^2\delta}{dt^2} = \frac{\omega_0}{2H} (P_m – P_e) \), describes the motion of a synchronous machine rotor, where \( \delta \) is the rotor angle, \( \omega_0 \) is the synchronous angular velocity, \( H \) is the inertia constant, \( P_m \) is the mechanical power input, and \( P_e \) is the electrical power output. A higher inertia constant \( H \) leads to a slower rate of change of rotor angle during a disturbance, effectively increasing the system’s resilience and thus the critical clearing time. This is because a larger inertia means more kinetic energy is stored, which can be released to counteract the power imbalance during a fault, allowing the generator to recover its synchronism. Therefore, increasing the inertia constant directly enhances transient stability by providing a greater buffer against destabilizing forces. The Shanghai University of Electric Power Entrance Exam emphasizes a deep understanding of these core power system concepts, as they are foundational to the efficient and reliable operation of electrical grids. Understanding how physical parameters like inertia influence system dynamics is crucial for future power engineers.

The question probes the understanding of power system stability, specifically transient stability, in the context of a synchronous generator connected to an infinite bus through a transmission line. The critical clearing time (CCT) is the maximum time a fault can persist before the system loses synchronism. For a three-phase fault at the generator terminals, the system’s post-fault power transfer capability is significantly reduced. The swing equation, \( \frac{d^2\delta}{dt^2} = \frac{\omega_0}{2H}(P_m – P_e(\delta)) \), describes the rotor angle dynamics. During a fault, \( P_e \) is drastically reduced. The critical clearing time is determined by the point where the fault is cleared before the rotor angle reaches the point of maximum power transfer of the post-fault system, which is often approximated by the angle at which \( P_e(\delta) \) equals the mechanical power input \( P_m \). In this scenario, a three-phase fault at the generator terminals means the impedance of the transmission path becomes very high, effectively reducing the power transfer capability \( P_e \) to near zero during the fault. The initial rotor angle is assumed to be at the steady-state operating point corresponding to the pre-fault power transfer. When the fault occurs, the generator accelerates due to the imbalance between mechanical input power and electrical output power. The system remains stable if the fault is cleared before the rotor angle \( \delta \) reaches a critical angle \( \delta_{cr} \). This critical angle is typically the angle where the post-fault power-transfer capability curve intersects the mechanical power input line. For a fault at the generator terminals, the post-fault system is the infinite bus connected directly to the generator (or through a reduced impedance if there’s a transformer). The maximum power transfer in the post-fault scenario is limited by the generator’s internal impedance and the system impedance. The question asks about the most critical factor influencing the CCT. While the mechanical power input (\(P_m\)), the pre-fault power transfer (\(P_{e0}\)), and the inertia constant (\(H\)) all play roles in the swing equation and thus affect transient stability, the *post-fault* power transfer capability is the most direct determinant of how much the rotor angle can deviate before synchronism is lost. A lower post-fault power transfer capability means the generator will accelerate more rapidly for a given \(P_m\), and the critical angle \( \delta_{cr} \) will be reached sooner, thus reducing the CCT. Therefore, the ability of the system to transfer power *after* the fault is cleared is paramount in determining how long the fault can be tolerated.

The question probes the understanding of power system stability, specifically transient stability, in the context of a sudden load increase. Transient stability refers to the ability of a power system to remain synchronized after a large disturbance, such as a fault or a sudden change in load or generation. The critical clearing time (CCT) is a key parameter in transient stability analysis, representing the maximum duration a fault can persist before the system loses synchronism. In this scenario, a sudden load increase is analogous to a disturbance that can destabilize the system. The generator’s inertia, represented by its inertia constant \(H\), plays a crucial role in its ability to ride through such disturbances. Higher inertia means the rotor speed changes more slowly in response to torque imbalances, providing a greater margin for the system to recover. The power angle, \(\delta\), is the angular displacement between the rotor of a synchronous machine and a synchronously rotating reference phasor. A sudden load increase causes a decrease in the net accelerating power, leading to a deceleration of the rotor and a decrease in the power angle. The system remains stable if the rotor angle does not exceed a critical value before the system can be restored to a stable operating condition. Therefore, a higher inertia constant \(H\) directly contributes to a larger critical clearing time and enhanced transient stability, allowing the generator to better withstand the impact of the load perturbation. The question assesses the understanding of how fundamental machine parameters influence system dynamics under stress, a core concept in power systems engineering taught at Shanghai University of Electric Power.

The question probes the understanding of the fundamental principles of power system stability, specifically transient stability, in the context of a synchronous generator connected to an infinite bus. The core concept tested is how changes in mechanical input power and electrical output power affect the rotor angle and, consequently, the system’s ability to remain synchronized after a disturbance. Consider a synchronous generator connected to an infinite bus. The swing equation describes the rotor dynamics: \[ J \frac{d^2\delta}{dt^2} = P_m – P_e \] where \(J\) is the moment of inertia, \(\delta\) is the rotor angle, \(P_m\) is the mechanical input power, and \(P_e\) is the electrical output power. The power angle characteristic for a synchronous generator connected to an infinite bus is typically a sinusoidal function: \(P_e = P_{max} \sin(\delta)\), where \(P_{max}\) is the maximum power transfer capability. A disturbance, such as a fault, causes a sudden change in \(P_e\). If the fault is cleared, \(P_e\) returns to its pre-fault or a new steady-state value. The system’s transient stability depends on whether the rotor angle \(\delta\) returns to a stable equilibrium point or oscillates uncontrollably. The critical clearing time (CCT) is the maximum duration a fault can persist before the system loses synchronism. If the fault is cleared within the CCT, the generator will oscillate and eventually settle to a new steady state. If cleared beyond the CCT, the rotor angle will continue to increase, leading to loss of synchronism. The area under the power angle curve during the fault and post-fault period is crucial. The equal-area criterion states that for stability, the area between the accelerating power (\(P_m – P_e\)) and the decelerating power (\(P_m – P_{e,new}\)) must be equal during the swing. In this scenario, the generator is operating at a steady state with \(P_m = P_{e1}\). A fault occurs, reducing \(P_e\) to \(P_{e\_fault}\). The rotor accelerates. The fault is cleared, and \(P_e\) returns to \(P_{e2}\). For stability, the kinetic energy gained during acceleration must be dissipated during deceleration. This means the area under the \(P_m – P_e\) curve during acceleration must equal the area under the \(P_m – P_e\) curve during deceleration. The question asks about the condition for maintaining synchronism. This is directly related to the ability of the generator to recover from a disturbance. The most critical factor determining this recovery is the system’s ability to damp oscillations and return to a stable operating point. This damping is achieved by the generator’s ability to adjust its electrical output in response to changes in rotor angle, effectively counteracting the initial acceleration. The ability to absorb the kinetic energy gained during the fault and subsequent acceleration is paramount. Therefore, the generator’s capacity to generate sufficient electrical power to decelerate its rotor and return to synchronism is the key. This is directly linked to the concept of the generator’s capability to provide a decelerating torque, which is proportional to the difference between the mechanical input and the electrical output.

The question probes the understanding of grid stability and the impact of distributed energy resources (DERs) on power system inertia. In a synchronous generator-dominated grid, inertia is primarily provided by the rotating mass of the generators. This inertia acts as a buffer against sudden changes in frequency, resisting deviations caused by disturbances like load changes or generator outages. The Shanghai University of Electric Power Entrance Exam often emphasizes the evolving nature of power systems with increasing penetration of inverter-based resources (IBRs) like solar photovoltaics and wind turbines. While IBRs can provide grid-forming capabilities, their inherent lack of physical rotating mass means they do not contribute to system inertia in the same way as synchronous generators. Therefore, a significant shift towards IBRs without compensatory measures can lead to a reduction in overall system inertia. This reduced inertia makes the grid more susceptible to rapid frequency fluctuations, potentially compromising stability. Advanced concepts explored at Shanghai University of Electric Power Entrance Exam include virtual inertia emulation techniques, where IBRs are programmed to mimic the inertial response of synchronous machines, and the development of advanced control strategies to manage the dynamic behavior of grids with high IBR penetration. The question requires understanding that the fundamental physical principle of inertia is tied to mass in motion, and that replacing synchronous machines with IBRs, unless specifically designed with inertia emulation, inherently reduces this physical inertia.

The question probes the understanding of power factor correction in AC circuits, a fundamental concept in electrical engineering, particularly relevant to the curriculum at Shanghai University of Electric Power. Power factor is the ratio of real power (kW) to apparent power (kVA), representing how effectively electrical power is being used. A low power factor, often caused by inductive loads like motors, leads to increased current for the same amount of real power, resulting in higher I²R losses in transmission lines and equipment, and potentially penalties from utility companies. To improve the power factor, capacitors are typically added in parallel with the inductive load. Capacitors provide leading reactive power, which counteracts the lagging reactive power consumed by inductive loads. The goal is to bring the overall power factor closer to unity (1.0). Consider a scenario where a facility at Shanghai University of Electric Power has an inductive load drawing \(100 \, \text{kW}\) at a power factor of \(0.7\) lagging. The apparent power is \(S = \frac{P}{\text{PF}} = \frac{100 \, \text{kW}}{0.7} \approx 142.86 \, \text{kVA}\). The reactive power consumed by the load is \(Q_L = \sqrt{S^2 – P^2} = \sqrt{(142.86 \, \text{kVA})^2 – (100 \, \text{kW})^2} \approx 102.0 \, \text{kVAR}\). The desired power factor is \(0.95\) lagging. At this new power factor, the real power remains \(100 \, \text{kW}\). The new apparent power would be \(S’ = \frac{P}{\text{PF}’} = \frac{100 \, \text{kW}}{0.95} \approx 105.26 \, \text{kVA}\). The new reactive power required is \(Q_{L}’ = \sqrt{(S’)^2 – P^2} = \sqrt{(105.26 \, \text{kVA})^2 – (100 \, \text{kW})^2} \approx 32.0 \, \text{kVAR}\). The capacitor bank needs to supply the difference in reactive power: \(Q_C = Q_L – Q_{L}’ = 102.0 \, \text{kVAR} – 32.0 \, \text{kVAR} = 70.0 \, \text{kVAR}\). Therefore, a capacitor bank of approximately \(70 \, \text{kVAR}\) is required to improve the power factor from \(0.7\) to \(0.95\). This demonstrates the practical application of reactive power compensation, a crucial skill for electrical engineers graduating from Shanghai University of Electric Power, enabling them to design efficient and cost-effective power systems. The ability to calculate and implement such corrections directly impacts operational efficiency and adherence to grid regulations, aligning with the university’s emphasis on applied knowledge and industry relevance.

The question probes the understanding of the fundamental principles governing the operation of a synchronous generator, specifically focusing on the impact of excitation current on its performance characteristics. A synchronous generator’s power factor is intrinsically linked to its excitation level. When the excitation current is increased beyond the level required for unity power factor operation at a given load, the generator becomes over-excited. This over-excitation causes the generator to deliver reactive power to the grid, leading to a leading power factor at its terminals. Conversely, under-excitation results in the generator absorbing reactive power, causing a lagging power factor. The question asks about the consequence of increasing excitation current while maintaining a constant mechanical input and load. With increased excitation, the armature current will decrease, and the power factor will shift towards leading. The voltage regulation, which is the change in terminal voltage from no-load to full-load, is also affected by excitation. However, the most direct and defining consequence of over-excitation, as described, is the shift towards a leading power factor. The terminal voltage might increase slightly or remain relatively stable depending on the grid’s characteristics and the generator’s design, but the primary observable effect on the power factor is the leading characteristic. The efficiency might also be affected due to increased copper losses in the field winding, but the power factor shift is a more direct and universally recognized outcome of manipulating excitation. Therefore, the most accurate description of the consequence of increasing excitation current in a synchronous generator operating at a constant mechanical input and load is that it will operate at a leading power factor.

The question probes the understanding of the fundamental principles governing the integration of renewable energy sources into a national grid, specifically focusing on the challenges and solutions relevant to the Shanghai University of Electric Power’s curriculum, which emphasizes smart grids and sustainable energy systems. The core concept here is grid stability and power quality when dealing with intermittent generation. The scenario describes a significant increase in solar photovoltaic (PV) capacity connected to the grid. Solar PV, being a voltage-source converter (VSC) based technology, can inherently provide reactive power support and voltage regulation. However, the *rate of change of power output* (ramp rate) due to fluctuating solar irradiance (e.g., cloud cover) is a primary concern for grid stability. Rapid changes in PV output can lead to voltage fluctuations and frequency deviations, especially if not adequately managed. The question asks about the most effective strategy to mitigate these issues. Let’s analyze the options: * **Option a) Implementing advanced grid-forming control strategies for the new PV installations.** Grid-forming inverters actively control voltage and frequency, mimicking the behavior of synchronous generators. This allows them to provide inertia and robust voltage support, directly counteracting the destabilizing effects of rapid PV output changes and improving overall grid resilience. This is a cutting-edge solution that aligns with the advanced research at Shanghai University of Electric Power. * **Option b) Requiring all new PV systems to operate solely in grid-following mode with a fixed power factor.** Grid-following inverters synchronize with the grid voltage and frequency and inject active power. While they can be controlled to provide some reactive power, their ability to dynamically respond to rapid changes and provide inertia is limited compared to grid-forming inverters. A fixed power factor would not adapt to the dynamic needs of the grid during intermittent generation events. * **Option c) Mandating the installation of large-scale synchronous condensers at all major substations.** Synchronous condensers are effective for providing inertia and reactive power support. However, they are mechanical devices, less flexible than VSC-based solutions, and their deployment is costly and geographically constrained. While beneficial, they are not as directly responsive to the *specific* challenge of rapid PV ramp rates as advanced VSC controls. * **Option d) Limiting the total installed capacity of PV to 10% of the grid’s peak demand.** This is a conservative approach that avoids the problem by limiting the source of the issue. However, it severely restricts the integration of renewable energy, which is contrary to the goals of modern power systems and the research focus of Shanghai University of Electric Power. It does not offer a solution for integrating *more* renewables. Therefore, implementing advanced grid-forming control strategies is the most sophisticated and effective method to enhance grid stability and power quality in the face of increasing intermittent renewable generation, directly addressing the challenges of rapid output fluctuations. This approach leverages the capabilities of modern power electronics to create a more robust and flexible grid, a key area of study at Shanghai University of Electric Power.

The question probes the understanding of grid stability and the impact of distributed energy resources (DERs) on power system inertia. Inertia in a power system is the tendency of rotating masses (primarily synchronous generators) to resist changes in frequency. When a disturbance occurs, the stored kinetic energy in these rotating masses helps to maintain frequency stability. The integration of inverter-based resources (IBRs) like solar photovoltaics and wind turbines, which do not inherently possess the same rotating mass as synchronous generators, can reduce the overall system inertia. This reduction makes the system more susceptible to rapid frequency deviations following disturbances. The Shanghai University of Electric Power Entrance Exam often emphasizes the practical challenges and advanced concepts in power system operation and planning, particularly in the context of renewable energy integration. Understanding how to maintain grid stability with a high penetration of IBRs is a key area of focus. While IBRs can be programmed to provide synthetic inertia through advanced control strategies, their contribution is fundamentally different from the physical inertia of synchronous machines. The question requires evaluating which of the given options best describes the primary consequence of increased IBR penetration on grid stability, considering the reduction in physical inertia. Option (a) correctly identifies the reduction in system inertia as a primary consequence, leading to faster frequency deviations. This is a well-established phenomenon in power systems with high DER penetration. Option (b) is incorrect because while voltage stability is also a concern with DERs, the question specifically relates to frequency dynamics due to inertia. Option (c) is incorrect as increased inertia would generally improve frequency stability, not degrade it, and DERs typically reduce physical inertia. Option (d) is incorrect because while grid congestion can be an issue with DERs, it’s not the direct consequence of reduced inertia on frequency response. Therefore, the most accurate and fundamental impact on grid stability stemming from the reduced physical inertia of IBRs is the increased susceptibility to rapid frequency deviations.

The question probes the understanding of grid synchronization principles, specifically concerning the impact of phase angle differences on power flow. When a new generator is connected to an existing AC power grid, the synchronization process requires matching voltage magnitude, frequency, and phase angle. If the phase angle difference between the incoming generator and the grid is non-zero, a reactive power component will flow. Specifically, if the incoming generator’s phase angle leads the grid’s phase angle, reactive power will flow from the generator to the grid. Conversely, if the incoming generator’s phase angle lags, reactive power will flow from the grid to the generator. The magnitude of this reactive power flow is proportional to the sine of the phase angle difference and inversely proportional to the impedance between the generator and the grid. In this scenario, the incoming generator’s phase angle is \( \delta = 5^\circ \) ahead of the grid’s phase angle. Assuming a simplified system with a direct connection (negligible impedance for conceptual understanding, or a small impedance \(X\)), the reactive power injected into the grid by the generator can be approximated. A leading phase angle implies the generator is supplying reactive power. The question asks about the *primary* consequence of this phase difference during synchronization. While frequency and voltage magnitude mismatches cause transient oscillations and potential instability, the *immediate* and *direct* consequence of a phase angle difference, assuming frequency and voltage are otherwise matched for synchronization, is the flow of reactive power. The magnitude of this reactive power is related to \( \sin(\delta) \). A positive \( \delta \) (leading) means the generator is contributing reactive power to the grid. Therefore, the most direct and immediate impact of a leading phase angle difference during synchronization is the injection of reactive power into the grid. This reactive power flow helps to support the voltage profile of the grid at the point of connection. The other options are less direct or incorrect: active power flow is primarily determined by voltage magnitude difference and impedance, not solely phase angle difference; frequency mismatch would cause oscillations, but the question implies synchronization is being attempted; and voltage magnitude mismatch would also lead to power flow, but the question specifically highlights the phase angle. The fundamental principle is that a phase difference drives reactive power exchange.

The question probes the understanding of grid stability and the impact of distributed energy resources (DERs) on power system inertia. In traditional power systems, synchronous generators provide significant inertia, which resists changes in grid frequency. When a disturbance occurs (e.g., a sudden loss of generation), this inertia helps to slow down the rate of change of frequency (RoCoF), giving control systems time to respond. Distributed energy resources, particularly inverter-based resources (IBRs) like solar photovoltaics and wind turbines, often do not inherently contribute significant inertia to the grid. While advanced control strategies can enable IBRs to emulate inertia (synthetic inertia), their contribution is typically programmed and can be less robust than that of synchronous machines. A higher penetration of IBRs without adequate inertia emulation or other inertia support mechanisms (like synchronous condensers or grid-forming inverters) leads to a lower system inertia. A lower system inertia means that for a given power imbalance, the grid frequency will change more rapidly. This increased RoCoF can trigger protection relays prematurely, lead to instability, and make it more challenging for automatic generation control (AGC) and frequency containment reserve (FCR) to maintain frequency within acceptable limits. Therefore, a grid with a high penetration of IBRs and low inherent inertia is more susceptible to frequency deviations and instability following disturbances. The scenario describes a grid with a high proportion of inverter-based generation. This directly implies a reduction in the system’s inherent inertial response. The question asks about the primary consequence of this reduced inertia. Option a) correctly identifies the increased susceptibility to rapid frequency deviations and potential instability due to a lower rate of change of frequency. This is a direct consequence of reduced inertia. Option b) is incorrect because while voltage stability is important, the primary and most direct impact of reduced inertia is on frequency dynamics, not necessarily voltage magnitude fluctuations in the immediate aftermath of a disturbance, unless the disturbance itself is voltage-related or the system is already operating at voltage limits. Option c) is incorrect. Increased inertia would *improve* the grid’s ability to withstand frequency deviations, not worsen it. This option describes the opposite of the expected outcome. Option d) is incorrect. While grid congestion can be a related issue in power system operation, it is not the direct or primary consequence of reduced system inertia. Congestion relates to transmission capacity limitations, whereas inertia relates to the system’s dynamic response to power imbalances.

The question probes the understanding of power factor correction in AC circuits, a fundamental concept in electrical engineering, particularly relevant to the curriculum at Shanghai University of Electric Power. Power factor is the ratio of real power (kW) to apparent power (kVA), representing the efficiency of power utilization. A low power factor, often caused by inductive loads like motors, leads to increased current for the same amount of real power, resulting in higher I²R losses in transmission lines and requiring larger conductors and transformers. Capacitors are used to counteract the inductive reactance, thereby improving the power factor. To improve a lagging power factor (caused by inductive loads), capacitive reactance must be added to the circuit. The required reactive power from the capacitor bank (\(Q_C\)) can be calculated using the initial and desired power factors and the real power. Let \(P\) be the real power (in kW), \(PF_{initial}\) be the initial power factor, \(PF_{desired}\) be the desired power factor, \(Q_{initial}\) be the initial reactive power (in kVAR), and \(Q_C\) be the reactive power of the capacitor bank (in kVAR). We know that \(P = S \times PF\), where \(S\) is the apparent power. Also, \(S^2 = P^2 + Q^2\). Therefore, \(Q = \sqrt{S^2 – P^2}\). From \(P = S \times PF\), we get \(S = \frac{P}{PF}\). Substituting this into the equation for \(Q\): \(Q = \sqrt{\left(\frac{P}{PF}\right)^2 – P^2} = P \sqrt{\left(\frac{1}{PF}\right)^2 – 1}\) For the initial state: \(Q_{initial} = P \left( \sqrt{\frac{1}{PF_{initial}^2} – 1} \right)\) For the desired state: \(Q_{desired} = P \left( \sqrt{\frac{1}{PF_{desired}^2} – 1} \right)\) The reactive power to be supplied by the capacitor bank is the difference between the initial and desired reactive power: \(Q_C = Q_{initial} – Q_{desired}\) \(Q_C = P \left( \sqrt{\frac{1}{PF_{initial}^2} – 1} – \sqrt{\frac{1}{PF_{desired}^2} – 1} \right)\) Given: \(P = 500 \, \text{kW}\) \(PF_{initial} = 0.75\) (lagging) \(PF_{desired} = 0.95\) (lagging) Calculate \(Q_{initial}\): \(Q_{initial} = 500 \, \text{kW} \left( \sqrt{\frac{1}{0.75^2} – 1} \right) = 500 \, \text{kW} \left( \sqrt{\frac{1}{0.5625} – 1} \right) = 500 \, \text{kW} \left( \sqrt{1.7778 – 1} \right) = 500 \, \text{kW} \left( \sqrt{0.7778} \right) \approx 500 \, \text{kW} \times 0.8819 \approx 440.95 \, \text{kVAR}\) Calculate \(Q_{desired}\): \(Q_{desired} = 500 \, \text{kW} \left( \sqrt{\frac{1}{0.95^2} – 1} \right) = 500 \, \text{kW} \left( \sqrt{\frac{1}{0.9025} – 1} \right) = 500 \, \text{kW} \left( \sqrt{1.1080 – 1} \right) = 500 \, \text{kW} \left( \sqrt{0.1080} \right) \approx 500 \, \text{kW} \times 0.3286 \approx 164.30 \, \text{kVAR}\) Calculate \(Q_C\): \(Q_C = Q_{initial} – Q_{desired} \approx 440.95 \, \text{kVAR} – 164.30 \, \text{kVAR} \approx 276.65 \, \text{kVAR}\) The closest standard capacitor bank size is 275 kVAR. This process of power factor correction is crucial for optimizing energy efficiency and reducing operational costs in industrial settings, a key focus for graduates of Shanghai University of Electric Power. Understanding the relationship between real power, reactive power, and apparent power, and how to manipulate them through power factor correction, is essential for designing and operating electrical systems effectively. The university emphasizes practical application of theoretical knowledge, and this question directly tests that ability in a common engineering scenario.

The core principle at play here is the concept of **system inertia** within the context of power grid stability, specifically focusing on frequency response. When a sudden load disturbance occurs, the immediate reaction of the generators is crucial. The kinetic energy stored in the rotating masses of synchronous generators provides a buffer against rapid frequency changes. This stored kinetic energy, proportional to the square of the rotor speed and the moment of inertia, resists changes in rotational speed, and thus frequency. Consider a generator with a moment of inertia \(J\) and operating at a synchronous speed \(\omega_s\). The kinetic energy stored is \(KE = \frac{1}{2} J \omega_s^2\). When a load disturbance causes a power imbalance \(\Delta P\), the generator’s rotor speed changes according to the swing equation: \(J \frac{d^2\theta}{dt^2} = P_m – P_e\), where \(\theta\) is the rotor angle, \(P_m\) is mechanical power input, and \(P_e\) is electrical power output. A change in frequency \(\Delta f\) is directly related to the change in rotor speed \(\Delta \omega\), where \(\Delta f = \frac{\Delta \omega}{2\pi}\). The rate of change of frequency (\(\frac{df}{dt}\)) is inversely proportional to the system inertia constant \(H\), which is defined as the kinetic energy at synchronous speed divided by the generator’s rated apparent power (\(S_{rated}\)): \(H = \frac{KE_{synch}}{S_{rated}}\). Therefore, \(\frac{df}{dt} \propto \frac{1}{H}\). A higher inertia constant \(H\) means a larger moment of inertia \(J\) relative to the generator’s rating, leading to a slower rate of frequency change for a given power imbalance. In the scenario presented, the Shanghai University of Electric Power’s grid experiences a sudden loss of a significant generating unit. This represents a negative \(\Delta P\) (a reduction in generation). Without immediate compensatory action from other generators, the grid frequency will drop. The rate at which this frequency drops is directly influenced by the total inertia of the connected synchronous generators. A grid with higher overall inertia (a larger sum of \(J\) for all connected generators, or a higher average \(H\)) will experience a slower frequency decline, allowing more time for control systems to respond and re-establish equilibrium. Conversely, a grid with lower inertia is more susceptible to rapid and potentially destabilizing frequency fluctuations. Therefore, the primary factor that would mitigate the immediate rate of frequency decline in such a scenario is the collective inertia of the remaining online synchronous generators.

The question probes the understanding of power system stability, specifically transient stability, which is crucial for the Shanghai University of Electric Power. Transient stability refers to the ability of a power system to remain synchronized after a major disturbance, such as a fault. The critical clearing time (CCT) is the maximum duration a fault can persist before the system loses synchronism. Beyond the CCT, the kinetic energy gained by the rotor during the fault exceeds the energy that can be absorbed by the system during the post-fault period, leading to instability. The scenario describes a synchronous generator connected to an infinite bus through a transmission line. A three-phase fault occurs, and the system’s ability to recover depends on how quickly the fault is cleared. The swing equation, \( \frac{d^2\delta}{dt^2} = \frac{\omega_0}{2H} (P_m – P_e) \), governs the rotor angle dynamics. During the fault, \( P_e \) (electrical power output) is significantly reduced. The acceleration area (integral of \( P_m – P_e \) over time) represents the increase in rotor kinetic energy. For stability, the deceleration area (integral of \( P_m – P_e \) after fault clearing, where \( P_e \) is restored) must be sufficient to bring the rotor back to synchronism. The CCT is the time at which the area under the \( P_m – P_e \) curve during the fault equals the maximum possible area that can be absorbed by the system after the fault is cleared. The question asks about the fundamental principle governing the determination of the critical clearing time. This time is intrinsically linked to the energy balance within the synchronous machine’s rotor during and after a disturbance. Specifically, it’s the point where the accumulated kinetic energy due to the power imbalance during the fault cannot be dissipated by the system’s restoring power after the fault is removed. Therefore, the critical clearing time is the maximum fault duration for which the system can regain synchronism, determined by the area under the power-angle curve.

The question probes the understanding of power system stability, specifically transient stability, in the context of a sudden load increase. Transient stability refers to the ability of a synchronous machine to remain in synchronism after a sudden disturbance. A sudden increase in load on a power system is a common disturbance. The critical clearing time (CCT) is the maximum duration a fault can persist before the system loses synchronism. However, this question is about a load increase, not a fault. A sudden load increase causes a decrease in the net electrical power output of generators, leading to a deceleration of their rotors. If this deceleration is significant and sustained, it can lead to a loss of synchronism. The ability of the system to withstand this disturbance depends on the inertia of the rotating masses, the damping coefficients, and the magnitude of the load increase relative to the system’s capacity. The concept of “inertia constant” (\(H\)) is crucial here. It represents the stored kinetic energy in the rotating machinery. A higher inertia constant means more stored energy, which can absorb a sudden change in power flow more effectively, slowing down the rate of change of rotor angle. The “power angle” (\(\delta\)) is the angular displacement between the rotor of a synchronous machine and a synchronously rotating reference phasor. A sudden load increase causes \(\delta\) to increase. The system remains stable if \(\delta\) does not exceed a critical value. The rate at which \(\delta\) changes is influenced by the inertia constant and the power system stabilizer (PSS) settings, which are designed to provide damping. Considering the options: 1. **Increased inertia constant:** A higher inertia constant (\(H\)) means that for a given change in power, the change in rotor speed (and thus the rate of change of rotor angle) will be smaller. This directly enhances transient stability by providing a buffer against rapid angular deviations. This is a fundamental principle in power system dynamics. 2. **Reduced damping coefficients:** Damping coefficients represent the energy dissipation mechanisms in the system, such as resistance and magnetic losses. Reduced damping means less energy is dissipated for a given change in speed, which would *exacerbate* instability and make the system *less* resilient to load changes. 3. **Lower generator saliency ratio:** Saliency refers to the difference in magnetic reluctance along the direct and quadrature axes of a synchronous machine. While saliency affects the synchronous reactance and thus the power transfer capability, its direct impact on the *transient stability margin* against a sudden load increase is secondary compared to inertia and damping. It’s more related to steady-state power transfer limits and voltage stability. 4. **Increased excitation system response time:** A faster excitation system (lower response time) can help restore the generator’s terminal voltage and power output more quickly after a disturbance. This is beneficial for transient stability, but the question asks about the *most* effective way to improve stability against a *sudden load increase*. Inertia provides an immediate, passive buffer against the initial acceleration, which is paramount in the very first moments of the disturbance. While a fast excitation system is important, the inertia constant’s role in mitigating the initial rate of change of rotor angle is more direct and fundamental for this specific type of disturbance. Therefore, increasing inertia is generally considered a primary method to improve transient stability against sudden load changes. The calculation for the change in rotor angle is complex and involves solving differential equations. However, conceptually, the acceleration equation for a synchronous machine is given by: \[ \frac{2H}{\omega_s} \frac{d^2\delta}{dt^2} = P_m – P_e \] where \(H\) is the inertia constant, \(\omega_s\) is the synchronous speed, \(P_m\) is the mechanical power input, and \(P_e\) is the electrical power output. A sudden load increase means \(P_e\) decreases instantaneously. A larger \(H\) directly reduces the acceleration \(\frac{d^2\delta}{dt^2}\), thus slowing down the rate at which \(\delta\) deviates from its steady-state value, thereby improving transient stability.

The core concept tested here is the understanding of **power factor correction** in AC circuits, a fundamental topic in electrical engineering, particularly relevant to the curriculum at Shanghai University of Electric Power. Power factor represents the ratio of real power (kW) to apparent power (kVA). A low power factor, often caused by inductive loads (like motors), leads to increased current for the same amount of real power delivered, resulting in higher line losses and reduced system efficiency. To improve the power factor, capacitive loads are introduced to counteract the inductive reactance. The goal is to bring the power factor closer to unity (1.0). The question asks to identify the most appropriate method for improving the power factor of a large industrial facility, which is a common scenario in power system analysis. The calculation for determining the required reactive power (kVAR) of the capacitor bank involves understanding the relationship between real power (P), apparent power (S), power factor (PF), and the angle \( \phi \). Initial power factor \( PF_1 = 0.75 \). Desired power factor \( PF_2 = 0.95 \). Real power \( P = 500 \text{ kW} \). The angle \( \phi_1 \) corresponding to \( PF_1 \) is \( \phi_1 = \arccos(0.75) \approx 41.41^\circ \). The angle \( \phi_2 \) corresponding to \( PF_2 \) is \( \phi_2 = \arccos(0.95) \approx 18.19^\circ \). The reactive power consumed by the load is \( Q_1 = P \tan(\phi_1) \). \( Q_1 = 500 \text{ kW} \times \tan(41.41^\circ) \approx 500 \text{ kW} \times 0.8819 \approx 440.95 \text{ kVAR} \). The desired reactive power after correction is \( Q_2 = P \tan(\phi_2) \). \( Q_2 = 500 \text{ kW} \times \tan(18.19^\circ) \approx 500 \text{ kW} \times 0.3287 \approx 164.35 \text{ kVAR} \). The required reactive power to be supplied by the capacitor bank is \( Q_c = Q_1 – Q_2 \). \( Q_c \approx 440.95 \text{ kVAR} – 164.35 \text{ kVAR} \approx 276.6 \text{ kVAR} \). The closest standard capacitor bank size is 275 kVAR. Therefore, installing a capacitor bank of approximately 275 kVAR is the correct approach. This method is standard practice for improving the power factor of industrial loads characterized by inductive components. The explanation emphasizes the efficiency gains, reduced line losses, and improved voltage regulation that result from power factor correction, all critical considerations in power system operation and design, aligning with the advanced studies at Shanghai University of Electric Power. The choice of a fixed capacitor bank is generally suitable for loads with relatively stable inductive characteristics, whereas dynamic compensation might be considered for highly variable loads, but for a large industrial facility with predominantly motor loads, a fixed bank is a common and effective solution.

The question probes the understanding of the fundamental principles of distributed generation integration into power grids, specifically focusing on the impact of inverter-based resources (IBRs) on grid stability and control. The core concept here is the difference in inertia response between synchronous generators and IBRs. Traditional synchronous generators possess inherent mechanical inertia due to their rotating mass, which helps to dampen frequency fluctuations. IBRs, such as those used in solar and wind power, typically do not have this mechanical inertia. While advanced control strategies for IBRs can emulate inertia through virtual inertia control, this is an active control mechanism that requires sensing frequency deviations and adjusting power output accordingly. It is not an inherent property. Therefore, a grid with a higher penetration of IBRs without advanced inertia emulation will exhibit a reduced overall system inertia, leading to faster and more significant frequency deviations following disturbances. This makes the grid more susceptible to instability and requires more sophisticated control to maintain frequency within acceptable limits. The Shanghai University of Electric Power, with its focus on power systems and renewable energy integration, would emphasize this nuanced understanding of grid dynamics.

The question probes the understanding of power system stability, specifically transient stability, in the context of a sudden load increase. Transient stability refers to the ability of a synchronous machine to remain in synchronism after a large disturbance. A sudden increase in load on a power system is a significant disturbance. The critical clearing time (CCT) is the maximum duration a fault can persist before the system loses synchronism. While the question doesn’t involve a fault, a sudden load increase can be analyzed using similar principles of rotor dynamics. The swing equation, \( \frac{2H}{\omega_s} \frac{d^2\delta}{dt^2} = P_m – P_e \), describes the rotor angle dynamics. \(P_m\) is the mechanical power input, and \(P_e\) is the electrical power output. When load increases suddenly, \(P_e\) increases instantaneously, causing a deceleration of the rotor (negative \( \frac{d^2\delta}{dt^2} \)). The system’s ability to recover depends on the kinetic energy stored in the rotating masses and the damping present. The concept of “equal area criterion” is fundamental to transient stability analysis. It states that for a system to remain stable after a disturbance, the area under the power-angle curve during the deceleration period must be less than or equal to the area under the curve during the acceleration period. In this scenario, the sudden load increase causes a drop in \(P_e\), leading to rotor deceleration. The system will remain stable if the rotor angle does not exceed a critical value, which is determined by the initial operating point and the system parameters. The ability to withstand this disturbance without losing synchronism is directly related to the system’s inherent inertia and damping characteristics. Higher inertia (represented by \(H\)) provides more resistance to changes in rotor speed, thus improving stability. Effective damping mechanisms, which dissipate kinetic energy, also play a crucial role. Therefore, the system’s resilience to a sudden load increase is primarily governed by its inertial response and the effectiveness of damping controls.

The core principle tested here is the understanding of electromagnetic induction and Lenz’s Law in the context of power generation, a fundamental concept at Shanghai University of Electric Power. When a conductor moves through a magnetic field, an electromotive force (EMF) is induced. Lenz’s Law dictates that the direction of this induced current will oppose the change in magnetic flux that produced it. In a generator, the rotating coil is constantly changing its orientation relative to the magnetic field, leading to a continuous change in magnetic flux. This induced EMF drives a current. The mechanical work done to rotate the coil against the magnetic forces (which arise from the interaction of the induced current with the magnetic field) is converted into electrical energy. Therefore, the efficiency of a generator is directly related to how effectively it converts mechanical input into electrical output, minimizing losses due to factors like resistance (Joule heating) and eddy currents. A higher induced EMF for a given rate of change of flux and magnetic field strength, coupled with minimal resistive losses in the windings and core, leads to greater electrical power output for a given mechanical input, thus higher efficiency. The question probes the understanding that the induced EMF is the direct consequence of the rate of change of magnetic flux, a key tenet of Faraday’s Law of Induction, and that this EMF is what drives the electrical output, with efficiency being a measure of the quality of this conversion process.

The question probes the understanding of the fundamental principles governing the operation of synchronous generators, specifically focusing on the impact of excitation current on their performance characteristics. A synchronous generator, when operating in parallel with a power grid, can be made to operate at leading, lagging, or unity power factor by adjusting its field excitation. At unity power factor, the synchronous generator is operating at its most efficient point in terms of reactive power generation or absorption. Increasing the excitation current beyond this point causes the generator to produce more leading reactive power, effectively acting as a capacitor. This leads to a decrease in the power angle (\(\delta\)) and an increase in the terminal voltage. Conversely, decreasing the excitation current causes the generator to absorb reactive power, operating at a lagging power factor. The “V-curve” for a synchronous generator graphically illustrates this relationship, plotting armature current against field excitation current for a constant real power output. The minimum point of the V-curve corresponds to unity power factor operation. Operating at a leading power factor (over-excitation) results in a higher armature current than at unity power factor for the same real power output, but with the advantage of supplying reactive power to the system, thereby improving the system’s voltage profile and stability. The question asks about the consequence of increasing excitation beyond the point where the generator is delivering real power at unity power factor. This action forces the generator to supply leading reactive power. This leads to an increase in the terminal voltage and a decrease in the power angle, while the real power output remains largely unchanged (assuming the prime mover input is constant and the grid can absorb the reactive power). The armature current will increase, but it will be leading the terminal voltage.

The question probes the understanding of grid stability and the impact of distributed energy resources (DERs) on power system inertia. Inertia in a power system is the stored kinetic energy in rotating synchronous generators. This inertia acts as a buffer against sudden changes in frequency, helping to maintain grid stability. When synchronous generators are replaced by inverter-based resources (IBRs) like solar photovoltaics and wind turbines, the system’s overall inertia decreases. This reduction in inertia makes the grid more susceptible to rapid frequency deviations following disturbances, such as the loss of a large generation unit or a sudden load increase. The Shanghai University of Electric Power Entrance Exam, with its focus on power systems engineering, would expect candidates to understand these fundamental concepts. The correct answer identifies the primary consequence of increased IBR penetration without advanced control strategies: a reduction in system inertia, leading to a more volatile frequency response. The other options, while potentially related to grid modernization, do not directly address the core issue of inertia reduction caused by the shift from synchronous generation to IBRs. For instance, enhanced voltage support is a benefit of advanced inverter controls, not a direct consequence of reduced inertia. Increased grid congestion is a separate issue related to transmission capacity. Improved power quality is a general goal, but not the specific impact of inertia reduction. Therefore, understanding the physical principle of inertia and its relationship to generation technology is key.