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Conference Paper

NREL/CP-5D00-72284

February 2019

Quasi-Static Time Series PV Hosting 

Capacity Methodology and Metrics

Preprint

Akshay Kumar Jain, Kelsey Horowitz, Fei Ding, 

Nicolas Gensollen, Barry Mather, and Bryan Palmintier

National Renewable Energy Laboratory

Presented at the 2019 IEEE Conference on Innovative Smart Grid 

Technologies (IEEE ISGT)

Washington, D.C.

February 17–20, 2019
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Conference Paper

NREL/CP-5D00-72284

February 2019

Quasi-Static Time Series PV Hosting 

Capacity Methodology and Metrics

Preprint

Akshay Kumar Jain, Kelsey Horowitz, Fei Ding, 

Nicolas Gensollen, Barry Mather, and Bryan Palmintier

National Renewable Energy Laboratory

Suggested Citation

Jain, Akshay Kumar, Kelsey Horowitz, Fei Ding, Nicolas Gensollen, Barry Mather, and Bryan 

Palmintier. 2019. Quasi-Static Time Series PV Hosting Capacity Methodology and Metrics: 

Preprint. Golden, CO: National Renewable Energy Laboratory. NREL/CP-5D00-72284.

https://www.nrel.gov/docs/fy19osti/72284.pdf.
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Quasi-Static Time-Series PV Hosting Capacity 

Methodology and Metrics

Akshay Kumar Jain1, Kelsey Horowitz2, Fei Ding1, Nicolas Gensollen1, Barry Mather1, Bryan Palmintier1

1

Power System Engineering Center, 2Strategic Energy Analysis Center 

National Renewable Energy Laboratory

Golden, CO, US

Abstract— Distributed photovoltaic systems (DPV) can cause 

adverse grid impacts, including voltage or thermal violations. The 

installed capacity at which violations first occur and above which 

would require system upgrades is called the hosting capacity. 

Current methods for determining hosting capacity tend to be 

conservative by either only considering infrequent worst-case 

snapshots in time and/or only capturing coarse time and spatial 

resolution. Additionally, current hosting capacity methods do not 

accurately capture the time-dependence making them unable to 

capture the behavior of voltage regulating equipment and of some 

advanced controls mitigations. This can trigger delays from 

unnecessary engineering analysis or deter solar installations in 

areas that are actually suitable. We propose a quasi-static-timeseries (QSTS) based PV hosting capacity methodology to address 

these issues. With this approach, we conduct power flow analysis 

over the course of a full year, to capture time-varying parameters 

and control device actions explicitly. We show that this approach 

can more fully capture grid impacts of DPV than traditional 

methods.

Index Terms- PV Hosting Capacity, Quasi-Static Time-Series

Simulation, System Impact Studies

I. INTRODUCTION 

The widely used practice for determining a feeder’s 

photovoltaic (PV) hosting capacity, or the amount of PV the 

feeder can host without adverse grid impacts that might require 

changes or upgrades to the distribution system, tries to find the 

minimum limits for a given spatial deployment of Distributed 

photovoltaic systems (DPVs) [1]-[3]. The analysis is historically 

conducted at worst-case time points (snapshots) of maximum or 

minimum load or the maximum PV to load ratio. We refer to 

these as “static, snapshot hosting capacity” methods. In this 

approach, the first parameter violated determines the hosting 

capacity and is often the upper voltage limit as per ANSI 

standard C84.1-2016, Range A [4]. However, this ANSI 

standard also allows infrequent violations of the voltage limit as 

long as they are corrected [4]. Operation of voltage control 

devices, such as capacitors and regulators, can bring the voltages 

within limits in a short time span. However, static hosting 

capacity metrics cannot capture such changes in the control 

device operations, a potential limit to hosting capacity, and 

therefore use proxy metrics, such as not allowing any equipment 

operations.

Thus, the resulting estimates of hosting capacity using static, 

snapshot methods provide a conservative estimate of how much 

DPV could be hosted on a given system without upgrades. 

Additionally, the use of snapshot analyses does not allow for one 

to capture how certain system changes that may be lower cost, 

for example dynamically changing the set points of PV inverters 

for voltage regulation or selective curtailment, that can be used 

to expand the hosting capacity.

Quasi-static time-series simulation (QSTS) is one option to 

better reflect the behavior of PV, grid devices, or loads to more 

accurately capture potential system impacts and hosting 

capacities. QSTS analysis has been previously used for 

conducting impact studies of control schemes for smart inverters 

and voltage regulating devices [5]-[7].

Recently, “iterative” hosting capacity techniques have 

introduced some time-varying simulation, such as the use of two 

representative 24-hour periods, that begin to address these issues 

[8,9]. However, the computational challenges have limited the 

efforts to use long (e.g. hourly) timesteps that may not accurately 

capture cloud-induced variability or corresponding regulator and 

capacitor control responses, which typically require 1 minute or 

faster analysis for lower errors [7]. Such efforts also tend to 

resort to reduced representations (e.g. only 3-phase lines) of the 

distribution feeder that can also miss some phenomena, 

particularly for smaller DPV.

This paper overcomes these gaps by proposing a full QSTSbased hosting capacity approach. Recent algorithmic advances 

promise to drastically speed QSTS simulations (e.g. [10]) , so we 

focus on describing key considerations for using QSTS for 

hosting capacity, defining candidate metrics, and comparisons to 

traditional static methods. It can be difficult to provide a single 

set of metrics for QSTS hosting capacity, since it will be 

determined by the comfort level of utilities in allowing voltage 

deviations or thermal violations on their system for small periods 

of time, and also because the preferences or practices vary 

significantly between utilities. However, exploring potential 

definitions of QSTS hosting capacity and carefully analyzing the 

time-series impacts of DPV on distribution networks can help in 

achieving a more sophisticated understanding of hosting 

capacity and how it may be expanded to incorporate increased 

DPV penetration in the future.

This paper aims to provide initial insights into these issues 

by exploring QSTS hosting capacity. Section II introduces a 

QSTS hosting capacity methodology, and an example set of 

metrics that could be used to understand hosting capacity in a 

QSTS world. Section III compares results between snapshot PV 

hosting capacity and QSTS PV hosting capacity on a real 

distribution feeder in the United States using 1-minute resolution 

load and PV profiles simulated for a one-year period.

II. QSTS PV HOSTING CAPACITY

Per the draft IEEE guide, QSTS simulation,

“refers to a sequence of steady-state power flow, conducted 

at a time step of no less than 1 second but that can use a time 

step of up to one hour. Discrete controls, such as capacitor 

switch controllers, transformer tap changers, automatic 
2 

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switches, and relays, may change their state from one step to the 

next. However, there is no numerical integration of differential 

equations between time steps.” [11] 

Thus, to get the most accurate PV hosting capacity results, 

the QSTS simulations should be conducted at a time resolution 

that can adequately capture the time delays of the voltage control 

devices (typically about 30 seconds) for at least one full year. 

However, in practice this can be difficult to achieve. 

First, annual load and PV profiles for a distribution feeder at

second or minute time resolution are difficult to obtain and are 

often not available. The increasing use of advanced metering 

infrastructure by utilities has allowed for more data to be 

available than before, but data integrity and availability issues 

remain in many cases. Secondly, once the finer time resolution 

load profiles are available, the analysis itself poses major 

computational challenges. For a real distribution model with 

thousands of nodes and 1 second resolution load and PV data, an

annual simulation could take a few days. In order to achieve 

realistic PV hosting capacity results, multiple deployments at 

each PV penetration level must be analyzed. This could easily 

push the analysis duration to several years. A variable time step 

(VTS) solver proposed in [10] can be used to narrow down the 

number of time points to be analyzed by using a larger and a finer 

resolution step size. The solver has been shown to reduce the 

simulation time by up to 90% with 1-second resolution data in 

some cases [10]. The various deployment and penetration 

scenarios can be simulated using the VTS solver in parallel on a 

high-performance computing system, potentially reducing the 

simulation time to a few days even with 1-second resolution 

data. However, the VTS solver was not used in the case study 

discussed in this paper as the finest time resolution available for 

the load and PV profiles was 1-minute and all data points could

be analyzed in a relatively short duration. 

Defining a set of rules or metrics for determining the QSTS 

PV hosting capacity poses its own unique challenges. Applying 

static PV hosting capacity metrics, such as instantaneous voltage 

and thermal violations, to a QSTS simulation would counter the 

very purpose of performing a QSTS study, because the results 

would be the same as the snapshot hosting capacity case, and the 

fact that in practice, for example, the voltage is allowed to be 

outside of ANSI A limits for a short duration of time will not be 

captured. So, a new set of metrics will have to be defined that

conform more closely with the established standards and can 

allow infrequent parameter violations, provided they are 

corrected in a timely manner. 

A. QSTS PV hosting capacity metrics 

The proposed metrics for evaluating QSTS PV hosting 

capacity are based on common standards and try to 

accommodate infrequent limit violations. These metrics can be 

applied independently to each PV deployment scenario. The 

amount of PV in the deployment scenario where any of these 

metrics are violated would be the feeder’s quasi-static PV 

hosting capacity. These metrics focus on the impact of time 

varying parameters on grid operations and not solely on the 

instantaneous values. The results in this section are for a day long 

simulation on a detailed distribution feeder model using 1-

minute resolution data. To bring out the differences in the 

metrics clearly, three utility scale DPV units are deployed on the 

three phase primary nodes near the feeder extremities, as shown

in Fig. 1. This feeder model has about 3500 nodes and includes 

secondaries. The capacity of the deployed PV units is varied to

highlight the limiting conditions of each metric. 

1) Voltage Metrics: ANSI standard C84.1-2016 defines two 

voltage ranges, A and B [4]. It allows infrequent, short-term 

voltages outside both ranges. However, during Range B 

violations, equipment might not operate satisfactorily and 

protective devices might operate to protect the equipment. 

Considering these issues two separate metrics were created: 

a) Moving n-minute average voltage: In this metric bus 

voltages are monitored using a n-minute moving window, the 

window length used here is 10 minutes and can be modified by 

a utility based on operational requirements. The moving 

average voltage of each bus for a 10 minute duration is 

determined and the maximum and minimum of these averages 

are stored for all the analyzed time points. If these values are 

outside Range A limits, the current time point tc is stored in a 

vector as summarized in algorithm 1. If the violations continue

until time point tf, the time violation would be tf - tc, as shown 

in Fig. 2. We assume that the total time violation should not be 

2 hours more than that in the base case for the entire year. 

Figure 3.a shows the maximum instantaneous and average 

voltages observed in a day long QSTS simulation of the test 

feeder of Fig. 1, with three utility scale PV units of 1 MW each. 

The results in the blue boxes show how the 10 minute moving 

average allows short term voltage violations, but captures the 

violations in a time vector (shown in green on the secondary 

axis) if the violations persist. The total time for which the 

moving 10 minute average voltages were outside range A was 

169 minutes, thereby violating this metric. 

Figure 1. Test Feeder topology and PV unit locations 

a) Instantaneous maximum voltages: The instantaneous 

voltages at any time point should not be outside Range B or, if

Range B is exceeded in the base, no PV case, then the number 

of these instantaneous violations with PV should never be more 

than those in the base case. There are a couple of overvoltage 

violations in Fig. 3.a, so this metric is also violated assuming 

base scenario did not have Range B violations.

Utility scale PV units 

Potential small rooftop PV locations 

Substation 
3 

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Figure 2. Moving n-minute average voltage metric 

2) Loading Metrics: The ampere rating of the lines and 

cables and kVA ratings of the distribution transformers are 

determined based on the load demand to be met. These ratings 

may be exceeded in feeders with high PV. The following two 

metrics are defined for quantifying the total thermal violations 

in a QSTS simulation, using a similar methodology as for 

voltages: 

a) Moving n-hour average loading: It has been suggested 

that an air-cooled transformer could be operated for up to 2 

hours at 120% of its rated capacity following an initial loading 

of 90% [12]. To comply closely with this rule, a 2 hour moving 

average of each transformer’s loading as a percentage of its 

rated capacity is calculated. If the maximum average loading 

exceeds 120%, the time vector is updated in a similar manner as

the moving n-minute average voltage metric. The total time 

violation should not be more than that in the base, no PV, 

scenario. For over-load conditions on lines a similar 

methodology is used, however the 2 hour average loading is not 

allowed to exceed 100% of the rated capacity as lines do not 

have any additional cooling mechanism. Fig. 3.b shows the 

maximum instantaneous and average line loadings observed 

when three, 2.5 MW utility scale PV units were deployed in the 

test feeder of Fig. 1. The results in the blue box show that using 

a 2-hour moving average allows short term over-loading, but 

captures long term violations. It can also be seen that similar to 

the voltage metric, the time vector is updated only when the 

loading exceeds the threshold. 

b) Instantaneous over-loading: The instantaneous 

loading of the transformers should not exceed 150% of their 

rated capacity, whereas for lines the maximum instantaneous 

loading threshold is 120%, or might be even lesser at 100% for 

some utilities. In Fig. 3.b, both of the line loading metrics are 

violated. 

Time Vector Violation

0 0

15 (tf2) 2 (tf2 - tc2)

14 0

13 (tc2) 0

0 0

11 (tf1) 1 (tf1 - tc1)

10 (tc1) 0

Time : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Store: All Bus V All Bus V All Bus V All Bus V All Bus V All Bus V All Bus V All Bus V All Bus V All Bus V All Bus V All Bus V All Bus V All Bus V All Bus V All Bus V Total_violation (mins) 3

10 min average >1.05 or 10 min average < 0.95 - store final time (16) else store (0)

if: 10 min average >1.05 or 10 min average < 0.95 - store final time (15); else: store (0)

if: 10 min average >1.05 or 10 min average < 0.95 - store final time (10); else: store (0)

if: 10 min average >1.05 or 10 min average < 0.95 - store final time (11); else: store (0)

if: 10 min average >1.05 or 10 min average < 0.95 - store final time (12); else: store (0)

if: 10 min average >1.05 or 10 min average < 0.95 - store final time (13); else: store (0)

if: 10 min average >1.05 or 10 min average < 0.95 - store final time (14); else: store (0)

Initialize total time = 1 year (525,600 minutes); 

B = set of all feeder buses; 

Tw = Window length (10 minutes); 

while (time < total time) do

 for b ε B do 

 ܸ௕ ൌ ଵ

்ೢ

෌ ܸ௕,௧

௧௜௠௘

௧ୀ௧௜௠௘ି்ೢ

 end 

 Vmax = Max (Vb,∀ܾ ∈ ܤ (

 Vmin = Min (Vb, ∀ܾ ∈ ܤ (

 if Vmax or Vmin outside Range A do 

 Store time in vector 

 end 

end 

Algorithm 1: Moving 10-minute average voltage metric 

 

Figure 3.a (top) Maximum instantaneous and average voltages, and violations captured in a time vector 

Figure 3.b (bottom) Maximum instantaneous and average percentage line loading, and violations captured in a time vector 

tfn

tcn
4

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Control Equipment Operations: High PV penetration can lead 

to frequent changes in the feeder voltages, potentially leading to 

increased state changes of the voltage control equipment such 

as voltage regulators and switched capacitors. These increased 

mechanical movements of the control equipment can reduce 

their life span. Thus, it is necessary to ensure that the control 

device operations are not increased significantly. Number of 

device movements can not be determined in the snapshot 

hosting capacity analysis, and thus this further highlights the 

need for conducting QSTS PV hosting capacity studies.

Future work is still needed to detemine how significant the 

issue of device movements is and what the implications are in 

terms of device lifetime and associated operation and 

maintenance (O&M) costs. Utilities may not use number of 

device movements as a metric for determining when a 

distribution upgrade is required, and thus this may not represent 

a hard limit on hosting capacity in practice. In this paper, we 

track the number of control device (regulators and capacitors) 

operations with PV compared to the base case in order to help 

provide additional insights on this topic. To analyze the impact 

of PV units on the operations of different types of voltage 

control devices, a substation load tap changer (LTC) and a 

voltage regulator were added to the feeder model shown in Fig.

1, in addition to the 5 existing capacitor banks. The number of 

regulator tap changes increased 62.5% and capacitor state 

changes increased 25% over the base scenario, for a day long 

simulation with 3, 1 MW PV units.

III. SNAPSHOT VS QSTS PV HOSTING CAPACITY

For conducting the snapshot PV hosting capacity analysis on 

the original feeder model of Figure 1, the added voltage regulator 

and substation LTC were removed. PV deployment scenarios 

were generated based on Monte Carlo simulation [3]. The 

potential locations where a small rooftop PV unit may be deployed 

are shown in Fig. 1. The type of the PV unit, residential or 

commercial, is determined based on the type of the randomly 

chosen customer load. Random sampling from probability density 

functions of both residential and commercial PV maximum 

powers acquired from the California solar PV statistics data was 

used to determine the PV unit size. This widely used methodology 

is described in [1]. All the PV inverters are operating in constant 

power factor mode, with a fixed set point of 0.95 inductive. The 

procedure is repeated to generate PV deployment scenarios 

covering 5% to 100% of the customers on the feeder, in a 5% step 

size. The study is repeated 10 times for each of these percentage 

penetration levels. Thus, a total of 200 scenarios were analyzed at 

the peak and minimum loading time points.

The minimum loading condition occurred during the solar 

peak hours (between 11 am – 1 pm) when there is a high PV to 

load ratio, leading to overvoltage violations as shown in Fig. 4. 

ANSI Range A was used as the conservative threshold because 

the snapshot PV hosting capacity methodology doesn’t provide 

any information about the time for which the violations might 

continue. The PV hosting capacity limit was reached for 

deployment 8 at 65 percent PV penetration as highlighted in Fig. 

4, where the maximum instantaneous voltages of each PV 

deployment scenario are plotted. Even though 65% of the 

customers were deployed with a PV unit, the net generation was

about 22% of the peak feeder load of 7.6 MVA.

Figure 4. Maximum instantaneous voltage observed in each deployment and 

PV penetration scenario of the snapshot PV hosting capacity study

To compare the results of the snapshot PV hosting capacity

study with QSTS PV hosting capacity, all the penetration levels 

for deployment 8 were analyzed using a yearlong QSTS PV 

hosting capacity study with 1-minute resolution load and PV 

profiles. As can be seen in Fig. 4, the results for different 

deployments are closely clustered. Thus, the QSTS PV hosting 

capacity value obtained from a single deployment, can be 

expected to be very close to the actual hosting capacity value. To 

test the impact of a different window length, a 5-minute moving 

average was used for the voltage metric while the remaining 

metric parameters and thresholds were kept the same as 

described in section II.A.

After significant code optimization in python, a single yearlong simulation took about 65 minutes on a Core i5-7300U 

processor operating at 2.60 GHz. Analyzing all 20 penetration 

levels necessary to compute the QSTS hosting capacity value in 

series would have taken more than a day. To overcome this issue, 

the different penetration levels were simulated in parallel on a 

high-performance computing system, and the QSTS PV hosting 

capacity results were obtained within a couple of hours.

The results from these year-long QSTS PV hosting capacity 

studies are shown in Fig. 5. Even when 100% of the customer 

locations were deployed with a PV unit, which have an aggregate 

rating of about 35% of the peak feeder load, no undervoltage or 

thermal violations were observed. The increase in the number of 

capacitor state changes is also well within the metric thresholds. 

The base scenario had Range A overvoltage violations (>1.05 

p.u.) for about 0.73% of the time points analyzed 

(3,868/525,600). However, these were only marginally above the 

threshold as only about 0.0057% of the time points were outside 

Range B (> 1.058 p.u.). The reason for Range B violations was 

sudden load drops as shown in Fig.6, which are not captured in 

the snapshot PV hosting capacity study. These events can cause 

a sudden spike in voltage, but it is quickly regulated by the 

voltage control devices. For the event shown in Fig. 6, the voltage 

spike was mitigated by the opening of a capacitor bank after its 

time delay setting of four minutes. The reduction in overvoltages 

in some of the PV scenarios from the base case is because of the 

reactive power support from the inverters operating at 0.95 

inductive power factor setting. The role of reactive power support 

in mitigating overvoltages was evident from a yearlong 

simulation of the 65% penetration scenario with all inverters 

operating at unity power factor, as it resulted in an increase in the 

overvoltages by about 134% from the base scenario.

0 500 1000 1500 2000 2500 3000

PV Penetration (kW)

1.035

1.04

1.045

1.05

1.055

1.06

1.065

p.u.

Maximum Voltage Magnitude v.s. PV Penetration

 

 

65% Pen. Level
5 

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The first metric to be violated was the 5-minute moving 

voltage average, when the total time violation was 2 hours more

than that in the base case for the entire year. However, this 

violation occurred at 100% PV penetration scenario, suggesting 

the possibility of deploying 35% more customer locations with 

PV units than the snapshot study proposed, without adversely 

affecting the grid or the need for system upgrades. 

IV. CONCLUSIONS

This paper presented a QSTS PV hosting capacity 

methodology and metrics. The methodology tries to conform 

more closely with the standards, by allowing infrequent shortterm parameter violations while capturing all long-term 

violations. This study methodology can give a better estimate of 

the feeder’s PV hosting capacity by considering the effect of 

voltage control device operations and their time delays. We 

have demonstrated this new methodology on a real feeder in the 

United States in this paper. While the snapshot PV hosting 

capacity gave a conservative estimate, the quasi-static PV 

hosting capacity suggested the possibility of going to a higher

PV penetration level. Although this paper focuses on the 

methodology itself, future work will delve on a more thorough 

validation of this approach by using a larger number of feeder 

test cases as well as running more scenarios in parallel. 

REFERENCES

[1] EPRI Distributed PV Monitoring and Feeder Analysis. Available at: 

http://dpv.epri.com/hosting_capacity_method.html. 

[2] D. Zhu, A.K. Jain, R. Broadwater, F. Bruna, “Feeder Voltage Profile 

Design for Energy Conservation and PV Hosting Capacity 

Enhancement,” Electric Power Systems Research, vol. 164, 2018. 

[3] F. Ding, B. Mather, N. Ainsworth, P. Gotseff, K. Baker, “Locational 

Sensitivity Investigation on PV Hosting Capacity and Fast Track PV 

Screening,” IEEE PES T&D Conference, 2016. 

[4] “Electric Power Systems and Equipment - Voltage Ratings (60 Hz),” 

ANSI C84.1-2016. 

[5] J.W. Smith, W. Sunderman, R. Dugan, and B.Seal, “Smart inverter

volt/var control functions for high penetration of PV on distribution 

systems,” 2011 IEEE/PES Power Syst. Conf. Expo. PSCE, 2011 

[6] Y. P. Agalgaonkar, B. C. Pal, and R. A. Jabr, “Distribution voltage 

control considering the impact of PV generation on tap changers and 

autonomous regulators,” IEEE Trans. Power Syst., vol. 29, 2014.

[7] M.J. Reno, J. Deboever, B. Mather, “Motivation and requirements

for quasi-static time series (QSTS) for distribution system analysis,” 

IEEE PES-GM, 2017. 

[8] J. Smith, “Methods and Considerations for Calculating Hosting 

Capacity,” presented at the IEEE PES General Meeting, Portland,

OR, 2018. 

[9] R. Salas, “California Hosting Capacity Analysis - Southern 

California Edison,” presented at the IEEE PES General Meeting, 

Portland, OR, 2018. 

[10]IEEE P1547.7 D110, “Draft Guide to Conducting Distribution 

Impact Studies for Distributed Resource Interconnection,” 2013.

[11]B. Mather, “Fast Determination of Distribution-Connected PV 

Impacts Using a Variable Time-Step Quasi-Static Time-Series 

Approach,” IEEE 44th Photovoltaic Specialists Conference (PVSC), 

2017. 

[12]“Permissible loading of oil-immersed transformers and regulators,” 

Facilities Instructions, Standards and Techniques, Vol. 1-5, US Dept. 

of Interior Bureau of Reclamation, 2000.

Figure 6. Voltage peak because of sudden load drop, quickly regulated

Figure 5. QSTS Results: (Top (a)) Number of overvoltage violations and total time for which the 5-minute average voltage was outside ANSI Range A; 

(Bottom left (b)) Sum of state changes of all capacitor banks; (Bottom right (c)) Maximum line and transformer loading observed at each PV penetration 

Snapshot: 

QSTS: 

QSTS first violation 

1.5

2

2.5

3

3.5

4

4.5

0.99

1.02

1.05

1.08

1 9 17 25 33 41 49 57 65 73 81 89

Load MVA

Voltage (p.u.)

Time points (Minutes of the day)

Max. Inst. voltage Min. Inst. voltage Load MVA