^{1}

^{1}

^{1}

Reliability results are important for proper planning and operation of utility companies. At the base of this method of analysis is the failure rate of the system components. In the traditional method, this probability of failure is determined by the components’ manufacturer and is considered to be constant. This study proposes a dynamic modeling of failure rate, taking the system operating conditions into consideration. With this new consideration, an IEEE test system has seven of its reliability indices quantified for comparison. The inclusion of the newly modeled failure rate leads to a worsening of 11.07% in the indices, on average. A second analysis is performed considering the presence of DG sources within the microgrid, namely PV and wind based. An improvement of 0.71% on the indices is noticed, once the DG sources are introduced. Finally, the effects of storage systems in the microgrid are investigated through a third scenario, in which two 2 MWh battery systems are introduced, and an improvement of 3.05% is noticed in the reliability indices.

It is expected of a reliable power system to be able to respond quickly and efficiently to faults, keeping customer disconnections to a minimum, both in quantities, as well as in duration. Billinton [

This traditional analysis has been applied to microgrids, regarding these systems as distributions systems with embedded microsources of generation. Bae et al. [

The aforementioned studies assume the failure rate of the system’s components to be constant, meaning that the probability that an element experiences a random fault is the same at all times, regardless of how the system is being operated. However, the current state of operation, i.e., the system’s current power flow, is expected to have an effect on the likelihood that one of its elements comes to a fault.

Xu et al. [

Voltage limits are set by ANSI regulations, while current limits are set by the manufacturers of each system component. This study considers faulted scenarios where these limits are not respected, to be faulted. The probability that the system’s power flow is such that these limits are surpassed, is taken into consideration in this study and adds to the system’s failure rate.

Once the reliability of the IEEE test system is quantified through a more traditional method of analysis [

The remainder of this paper is organized as follows: Section 2 discusses the mathematical modeling of both types of DG sources considered in this study (solar PV and wind), as well as the storage system. Also, the IEEE test system in which this basic analysis from [

The DG sources modeled in the microgrid, namely PV based and wind based are closely dependent of weather conditions, and are said to have intermittent output. Given that in this study, reliability analysis will be performed multiple times over a one year period, the changes in meteorological conditions will affect the power output of these DG sources and, as a consequence, the system’s power flow.

Wind generators have power injection dependent on wind speed. Three velocity levels are designed by the manufacturer of a specific generator model: cut-in speed, nominal speed, and cut-out speed. For wind velocities of less than the nominal value, the generator’s control will try to maximize the power absorbed from the wind by controlling the machine’s torque. For cases with very low wind speeds, below cut-in value, the system is not able to convert any energy, and the power output is brought to zero. On the other hand, for wind velocities higher than nominal value, the angle between the generator’s blades and the wind speed vector is adjusted by the controller, such that the power delivered is constant and at nominal value, as well as minimizing mechanical stresses, assuring that there won’t be any damages to the turbine. For cases with too high wind speeds, above cut-out speed, the controller will protect the blades and the power delivery will, again, be brought down to zero. This relationship is translated in Equation (1).

G_{RATE} being nominal power given by the manufacturer. V_{ci}, V_{RATE}, and V_{co} are the cut-in wind speed, nominal wind speed, and cut-out nominal speed, respectively [

Two main factors that influence the performance of a solar cell include temperature and solar radiation. In [

where, E_{RATE} and S_{RATE} are the rated temperature of operation and rated solar radiation, in which the manufacturer determines the cell’s parameters and performance.

Power and voltage supplied by a battery system have similar shape to what is shown in

Given that this study is focused on reliability performance in steady state, a rather simple model of battery was adopted. Characteristics such as the influence of temperature, and internal resistances were disregarded. Also, the storage capacity drops along the life span of a battery. Typical battery systems have life spans of the order of thousands of cycles [

of lower load, which is done at a slower rate than the rate of discharge. The charging demand for the batteries was set to 100 kW.

The test system adopted is presented in [

The protection scheme for this system is as follows: all feeders are considered to have one main breaker on its head, connecting it to the main source. Lateral distributors are protected by fuses. Disconnectors are present, and are capable to isolate any faulted section in the main distributor. Finally, all loads beyond the faulted point are transferred through the tie-line to an alternative feeder, as long as the second feeder is capable to handle the extra load. In terms of failure rate, a constant value of 0.065 failures/yr・km on all feeders is adopted. The time of unavailability, or repair time, is of 0.5 hours for loads that are transferred between feeders, 5 hours for loads that are disconnected, and 200 hours for faults on a transformer.

Multiple different indices are used to quantify reliability. In this study, seven of them are being calculated, according to Equations (4) through (10): System Average Interruption Frequency (SAIFI), System Average Interruption Duration (SAIDI), Customer Average Interruption Duration (CAIDI), Average Service Availability (ASAI), Average Service Unavailability (ASUI), Energy Not Supplied (ENS) and Average Energy Not Supplied (AENS). Reference [

where, λ_{i} is the failure rate of ith element; U_{i} is the unavailability of ith element, given by the product of failure rate and outage time, N_{i} is the number of customers connected to loadpoint i L_{i} is the average load on loadpoint i.

This section proposes a different approach on Failure Rate, considering it not only a simple constant, but a function of the current state of its distribution system, described by a power flow study. The resulting difference between this approach and the traditional reliability analysis will be evidenced in the next section, through the case study of the test system.

The power flow algorithm adopted was the Back/Forward Sweep Method, presented in [

A reliability study is normally performed on nominal conditions of operation. However, in an actual distribution system, the conditions might not always be ideal, and components might be subjected to different values of voltage or current than what they were designed for. A component subjected to a stress beyond its nominal ratings is expected to have a higher probability of failure. Also, steady state voltage limits are established by the ANSI to be a minimum of 0.95 pu and a maximum of 1.05 pu [

State variables are a set of variables used to summarize the system’s status. The state of a system, described by its state variables, is enough information to predict its future behavior, given that no external forces affect the system [

Thus, a function between Failure Rate and state variables is proposed, working as a link between power flow analysis and reliability analysis. The state variables, resulting of power flow analysis, will serve as input to the modeling, which will result in an updated value of Failure Rate, serving as input to the reliability analysis. This way, a more realistic result on reliability is expected to be achieved.

The standard failure rate is, therefore, added of a new probability of failure, related to the noncompliance of the limits established by the norm. This is represented in Equation (11) [

where, λ_{t}(x) is the new failure rate, λ_{o} is the random failure rate of 0.065 failures/km・yr, and P_{t}(x) is the additional probability of failure brought by the current state variables. Δt is the interval of time to be analyzed.

P_{t}(x) is quantified by Equation (12), where the integral element gives the cumulative distribution function (CDF) of state variable x, from zero to x_{s}. For x being either current or voltage, x_{s} gives the short term rating value, indicating the feeder’s capability in short term contingency operation [

It is assumed that state variable x follows a truncated normal distribution f_{t}(x), with mean value x set. The sensitivity factor α is introduced to characterize the relationship between mean value xset and normal rating value x_{n}. Therefore, α is given by the ration between xset and x_{n}. With the mean value defined, a third parameter β is introduced to determine the amount of dispersion of the normal distribution, and is given by Equation (13), where δ is the variance of function f(x). Parameter β is set to 5, while α is set to 1.3 for when state variable x represents current values, and 1.6 for when it represents voltage values

Reliability analysis will be performed for each hour within a one year period, in this study. In each period Δt, P_{t}(x) will be determined both for x being considered the system’s currents and the system’s voltages. The following reliability analysis will be performed for the worst case or, the highest of both modeled failure rates. The flowchart in

As shown in

Since [

Temperature and solar illuminance yearly profiles were obtained from measurements made by National Renewable Energy Laboratory, located in Oak Ridge, TN, throughout the year of 2014 [

the database of NASA’s Modern-Era Retrospective Analysis for Research and Applications [

_{o}.

ASAI is shown in

columns, and have their percentual impact indicated. The same is shown for the second scenario, in which the DG sources are introduced into the microgrid.

The initial assumption for the storage system was to connect them to two out of the same four LPs the DG sources were connected to. However, the reliability improvement was negligible. A new placement on nodes 44

Reference | Failure Rate Modeling | With DG | |||
---|---|---|---|---|---|

Index | Index | Gain (%) | Index | Gain (%) | |

SAIFI | 0.3 | 0.404 | +34.67 | 0.385 | −4.70 |

SAIDI | 3.47 | 3.82 | +10.09 | 3.78 | −1.05 |

CAIDI | 11.56 | 9.58 | −17.13 | 9.90 | +3.34 |

ASAI | 0.999604 | 0.999564 | −0.0040 | 0.999568 | +0.0004 |

ASUI | 3.96E−04 | 4.36E−04 | +10.10 | 4.31E−04 | −1.15 |

ENS | 54293 | 65068 | +19.85 | 64626 | −0.68 |

AENS | 11.36 | 13.62 | +19.89 | 13.52 | −0.73 |

Index | Without Storage | With Storage | Gain (%) |
---|---|---|---|

SAIFI (int/cus-yr) | 0.385 | 0.379 | −1.56 |

SAIDI (h/cus-yr) | 3.78 | 3.63 | −3.97 |

CAIDI (h/int) | 9.90 | 9.66 | −2.42 |

ASAI | 0.999568 | 0.999585 | +0.0017 |

ASUI | 4.31E−04 | 4.14e−04 | −3.94 |

ENS (MWh/yr) | 64626 | 61568 | −4.73 |

AENS (kWh/cus-yr) | 13.52 | 12.88 | −4.73 |

and 50 was proposed, as was shown in

The consideration of noncompliance of system state variables to the probability of failure (failure rate) resulted in worsening of all indices to a smaller or larger degree, with the exception of the CAIDI. The average impact was of a worsening of 11.07%, meaning that the traditional method or obtaining elements’ failure rates left certain factors out of the picture, which could result in considerable overestimations of system reliability. The introduction of DG sources within the microgrid and closer to the loads reduced the power flow intensity, mitigating the negative effects brought by the Failure Rate Modeling. However, this positive impact was rather small, having an average improvement of 0.71% over all seven indices, partially because the weather conditions were such that the DG sources operated below nominal power for most of the time. Also, given that the microgrid system was considered to be connected to an ideal infinity bus, the contribution of the DG sources was limited, for their larger impact would occur for faulted cases in the main grid, where the loads would be supplied only by the local generation. In those cases, the reliability indices would be deeply affected by the absence of DG sources. The last scenario aimed to investigate the impacts brought by storage systems, which would be responsible for balancing the irregular power injection profile of the DG sources caused by their weather dependent characteristics. These systems had an average contribution of 3.05% in the indices. Similar to the DG sources, the storage systems might have even higher impact if the possibility of fault in the main grid was being considered. For that case, a different logic of charge and discharge might need to be applied.

Valuable additions could be made to this study in the future: the failure rate modeling was only applied to cables and buses. The distribution transformers were also possible faulted elements, and might need to be considered. Second, a slightly more complete reliability analysis could be run, including the possibility of faults outside the microgrid, to which the system would respond by disconnecting itself and operating in off-grid mode. This would reduce the overall reliability of the system, but would better evidence the impacts of both the storage system and the DG sources. Lastly an optimal placement algorithm might be applied for the storage systems.

Rafael Medeiros,Xufeng Xu,Elham Makram, (2016) Assessment of Operating Condition Dependent Reliability Indices in Microgrids. Journal of Power and Energy Engineering,04,56-66. doi: 10.4236/jpee.2016.44006