### By Kiah Harris, PE, and Hyung Shin, Ph.D.

The electrical system in the United States is based on a frequency of 60 hertz. Utilities are required to keep the voltage oscillating at 60 hertz within a very close tolerance. A 60-hertz frequency indicates that the voltage is going through a complete cycle 60 times per second. Frequency can be maintained precisely at 60 hertz when there is exactly enough generation to meet the load (electrical demand) at that frequency.

The challenge utility operators face in accomplishing this task is that load tends to increase and decrease instantaneously. Utilities cannot predict with 100% accuracy what the load will be in the next instant. Because of this, generation is always reacting to load changes after the fact. This "chasing" of the load by generation leads to having too much generation compared to the load at certain times and too little at others. When there is excess generation, the frequency increases. When there is not enough generation, the frequency decreases.

### Renewable Energy Adds Challenges

The addition of renewable energy that is produced at the whims of nature, such as solar and wind, is an additional challenge to maintaining frequency. In these technologies, energy is produced when the sun is shining on solar panels or the wind is pushing against a propeller that turns a generator. The energy that is produced by these devices is not controllable by the system operators and is injected into the system as it is produced. The output can vary from zero to full output to zero if clouds go across the solar collector or the wind gusts. The varying output of these devices must be considered by the utilities that control the frequency, just as they consider variances in the load. These "non-dispatchable" energy producers can create significant challenges in operating a reliable system.

Utilities have a variety of generation sources to allow them to maintain the 60-hertz frequency as the load varies. Generation has characteristics such as the speed at which it can increase or decrease output, termed "ramp rate," that allow the frequency to be maintained in an acceptable range. Since utility operators cannot change the generation manually to respond to load and renewable output changes, an automatic system has been developed that collects data on the load and generation imbalance, analyzes how much it needs to adjust generation, and sends a signal to the generator to adjust its output either up or down as necessary. This process is performed every two to four seconds. The generators that respond to these signals are under automatic generator control (AGC).

The entity responsible for maintaining the system frequency through the use of AGC signals is called a balancing authority (BA). This BA can be an individual utility or a group of utilities.

### NERC Balancing Standard

One of the major standards that balancing authorities are required to comply with is the North American Electric Reliability Corporation's (NERC) BAL-001a. This standard develops the metrics by which balancing authorities are judged. The two control performance standard (CPS) factors are CPS1 and CPS2. The CPS performance standards established for utilities by the NERC state that the CPS1 rolling 12-month average shall not fall below 100%. The monthly average CPS2 is required to be above 90%. In order to comply with these standards, generation must be controlled through the AGC system to compensate for load variations. The addition of non-dispatchable renewable generation, can add significantly to the number of times generation is adjusted throughout the day.

The equations for the CPS performance include factors associated with the frequency deviations on the interconnected systems. The electric system in the United States is divided into three interconnections that operate independently of each other. The interconnections are shown in Figure 1. The frequency in each of these interconnections is different at any given moment. Connections between these interconnections are made through direct current systems.

The frequency performance of the U.S. electric system has been declining for a number of years. Lawrence Berkley National Laboratories published an analysis of the three interconnects in a December 2010 report, "Review of the Recent Frequency Performance of the Eastern, Western and ERCOT Interconnections." The report provided statistics about the decline of frequency performance.

Burns & McDonnell has investigated the CPS performance and how it can be impacted by the frequency deviations of the interconnection. The following discussion provides some insight on how a balancing authority could potentially improve CPS performance while reducing the number of generator adjustments provided to its units through AGC signals.

### Calculations for CPS1 and CPS2

NERC BAL-001a defines the CPS1 metric as a function of the 12-month rolling averages of the clock minute area control error (ACE) and the clock minute interconnect frequency deviation. CPS1 must be above 100% all the time. The CPS2 metric is a function of the frequency bias values of the balancing authority and the sum of all BAs in the interconnection. CPS2 has to be met 90% of the time.

#### CPS1

The clock minute average compliance factors (CF) are determined in accordance with the following equation:

CF clock minute average = (ACE/-10) * ΔF, where

ACE =(NI_{a}-NI_{s})-10B*(F_{a}-F_{s})-I_{ME}

NI_{a} is the actual net interchange,

NI_{s} is the scheduled net interchange,

B is the balancing authority's frequency bias term (B has a negative sign),

F_{a} is the interconnection actual frequency,

F_{s} is the interconnection scheduled frequency,

I_{ME} is the meter error

(insignificant and will be ignored from hereon),

and ΔF=(F_{a}-F_{s})

The above average is captured for each minute. These are then summed and divided by the number of acceptable minutes to develop the hourly averages. The hourly averages are then averaged across the month to get the monthly averages. The averages have to be less than a factor, which is a targeted constant frequency bound for the interconnect.

These averages are termed the compliance factor (CF). The CF is converted in to the CPS1 in accordance with the following:

CPS1=(2-CF)*100%

One can see that the interconnection frequency enters in to the CPS1 determination in the ACE and the ΔF factor and is influenced by the frequency bias and the targeted frequency bound. Through insertion of the ACE equation into the CF clock minute average equation and simplifying a bit, the following equation is developed:

Rigorously speaking, the net interchange control affects the frequency deviation. This has been the basis for control area operations for many years. However, from the standpoint of balancing authority size relative to the Eastern or Western interconnections, it is a reasonable assumption that adjustment by the BA's AGC to affect net interchange has minimal effects on the system frequency. Large BAs, such as the MISO and PJM, may approach the size where differences in net interchange could influence the frequency. In any event, ΔF is a common factor across the Eastern, Western and ERCOT interconnections and, as such, all of the BAs in the respective interconnect have the same ΔF value. The second term in the determination of CF is therefore a constant across all BAs in the interconnection. Consequently, a BA's AGC is affecting only the ΔNI factor of the first term.

The goal to maintain CPS1 compliance is to make CF as small as possible. The value of the second term is always positive regardless of whether the actual frequency in the interconnection is above or below the scheduled amount. If the first term is positive, then the terms would add and CF could be large. If it was negative, then CF would be reduced.

The value of the ΔNI*ΔF component becomes negative when the utility's difference in net interchange is of opposite sign to the difference in system frequency. This could happen, for instance, when the utility serves more power than the scheduled net interchange when the system frequency is above the scheduled frequency level. It is positive when both factors are of the same sign. Based on the sign of the factors, generation should be increased or decreased to move the actual values closer to the scheduled values. Table 1 provides the direction that generation output needs to move in order to respond to the sign of ΔNI and ΔF.

A quick inspection of Table 1 provides an indication that when the signs of the two factors are opposite, then the generation will be moved by the AGC in the direction that supports both the net interchange and the system frequency. When the signs are the same, the AGC will move the generation in a direction to support net interchange that is counter to what is needed for the larger interconnection.

Since most BAs by their adjustment of NI have minimal impact on the interconnect frequency, the BA can only adjust its NI to impact the CF term and thus its CPS1 performance. In looking at the equation for CF, if the first term is negative, this is in a direction to maximize the CPS1 by making CF smaller. Adjusting ΔNI toward zero through AGC would actually increase the CF term and reduce CPS1 performance. This indicates that if the signs of the ΔNI and ΔF terms are opposite, then no AGC action should be taken.

Since ΔF is defined as the difference between the actual and scheduled frequency, any sign-check algorithm considered should be verified to be checking against the scheduled frequency and not 60 hertz. Otherwise, CPS1 performance could suffer.

#### CPS2

CPS2 is a factor that monitors the magnitude of the average ACE across a 10-minute clock period. There are six non-overlapping periods per hour.

Ave_{10 min} ACE ≤ L_{10}

And, L_{10}=1.65ε_{10}√(-10B_{i})(-10B_{s})

Violations are the number of ACE clock 10-minute periods that are greater than L10. CPS2 must be met 90% of the time.

As the sign-check allows the AGC system not to act to reduce the net interchange deviation when the signs of the factors are opposite, there is a higher possibility of larger ACE values which may degrade CPS2. To alleviate this effect, an additional checking routine should be considered. When ΔNI and ΔF are in the opposite signs, the 10-minute average ACE then needs to be compared against L_{10} to make sure CPS2 compliance is maintained. If the 10-minute average ACE exceeds L_{10}, then the AGC system should act to reduce the net interchange deviation, even if the signs of the two terms are opposite.

### Analysis of One-Minute Records

Net interchange vs. frequency deviation diagrams can be used to determine how often the various combinations of signs of the ΔNI and ΔF condition might appear in a BA and if implementation of the sign-check algorithm would appear worthwhile. Figure 2 shows the points for one month for a utility in the Eastern Interconnection. Since the magnitude and timing of the load swings in the system for any instant are random, it is not possible to predict the location of any point on the graph.

The plot is useful to determine how often the ΔNI and ΔF terms are of the same or opposite sign. The plots are also useful to get an indication of the magnitudes of deviation in ΔNI and ΔF.

- The level of deviations in system frequency appears along the x axis. The more spread out the points are along the axis, the more difficult it can be to achieve compliance due to high ΔF values. The higher net-frequency deviations indicate a BA has less margin to improve CPS1 performance through affecting net interchange with AGC.
- The level of deviations in net interchange appears along the y axis. The more spread out the points are along the axis, the more generation has to be moved to maintain an acceptable level of ACE. The more points that a utility has in the second and fourth quadrants, the lower the level of AGC movement that is required to aid CPS1 compliance if the sign check is used.

The objectives of the sign-check scheme are to minimize AGC control adjustments when the signs are in the second and fourth quadrants and to increase the probability of points being in the second and fourth quadrants, thus increasing the CPS1 value with reduced AGC action.

Burns & McDonnell created a computer simulation of a utility where ACE factors were known. Knowing the reaction of the generators on AGC to signals calling for their adjustment due to ACE levels, the sign-check was applied to determine how the objectives were met. Figure 3 shows the graphs for the utility before the sign-check was applied and the simulation result after the sign-check. The number of points in the second and fourth quadrants where the signs are opposite was 48.9% of the total before the sign-check and 49.5% after the sign-check. For this month, the utility's CPS1 performance was approximately 124%, and the simulation result with the sign-check showed an improvement to 134%.

When considering the number of points in the second and fourth quadrants, AGC adjustments could be reduced to account for the opposite signs of the factors. Due to the requirements to check against the L_{10} factor, not all adjustments could be avoided. However, approximately 40% of the control actions could be avoided.

Utilities are always under pressure to minimize operating costs and risk of non-compliance with the NERC standards. The addition of non-dispatchable generation, such as wind and solar, increases the risk that the current generation mix of a utility will be unable to maintain CPS1 in acceptable ranges without significantly increasing the AGC operations on the units or installing units with faster ramp rates. The increase in frequency deviations in the interconnections also increase the challenges utilities have in remaining compliant.

Using the sign-check scheme outlined above provides another tool for a utility's AGC toolbox.

This algorithm check will potentially allow a utility to:

- Reduce its AGC operations to comply with CPS1.
- Increase the amount of non-dispatchable renewable generation on its system.
- Increase its margin to comply with CPS1 as the interconnection frequency varies from 60 hertz.

Burns & McDonnell can assist balancing authorities with this analysis.

Sign of Factor |
System Issue |
Generation Output |

ΔNI > 0 | Tie flow above schedule | Increase |

ΔNI < 0 | Tie flow below schedule | Decrease |

ΔF > 0 | Frequency above scheduled | Decrease |

ΔF < 0 | Frequency below scheduled | Increase |

### About the Authors

**Kiah Harris, PE,** is a department manager in the Burns & McDonnell Business & Technology Services Group in Kansas City. He earned his bachelor's and master's degrees at the University of Missouri-Columbia.

**Hyung Shin, Ph.D.,** is an associate electrical specialist in the Burns & McDonnell Business & Technology Services Group in San Francisco. He earned his bachelor's and master's degrees and doctorate in electrical engineering from Seoul National University, South Korea.