Distribution Systems, Distributed Energy Resources and Microgrids

Introduction

Electric-power distribution systems deliver energy from transmission or subtransmission networks to consumers. Traditionally, power flowed radially from substations through feeders to passive loads. Modern networks increasingly contain photovoltaic (PV) generation, wind generation, battery storage, electric-vehicle (EV) chargers, controllable demand and microgrids. These resources can reduce emissions and improve resilience, but they also introduce reverse power flow, voltage rise, uncertain loading, altered fault currents and coordination challenges.

Distribution engineering therefore combines circuit analysis, equipment planning, voltage control, reliability assessment, protection and operational optimization. Unlike a transmission network, a distribution system commonly has a high resistance-to-reactance ratio, substantial phase imbalance and many single-phase connections. Consequently, assumptions suitable for transmission studies cannot always be transferred directly to distribution studies.

Learning Objectives

After studying this chapter, students should be able to:

1. Distinguish radial, looped and meshed distribution structures.
2. Analyze balanced radial feeders using voltage-drop, loss and DistFlow models.
3. Explain substation, feeder and voltage-regulation functions.
4. Calculate standard distribution-reliability indices.
5. Assess the effects of distributed energy resources, EV charging and storage.
6. Explain distribution protection and its modification for bidirectional power flow.
7. Develop basic operating strategies for grid-connected and islanded microgrids.
8. Integrate technical, economic, regulatory and resilience criteria into distribution planning.

1. Distribution-System Architecture

A distribution system normally begins at a substation where transformers reduce voltage from transmission or subtransmission levels. Substation buses supply one or more medium-voltage feeders. Distribution transformers then supply low-voltage secondary circuits and service connections.

Figure: Main elements and bidirectional flows in a modern distribution system.

1.1 Network configurations

Radial systems provide one normal electrical path from a substation to each customer. They are economical and have relatively simple protection, but a single upstream fault can interrupt many downstream customers.

Looped systems contain alternative feeder paths but are often operated with a normally open tie switch. After a fault is isolated, the healthy portion can be transferred to another feeder, subject to thermal and voltage limits.

Meshed systems operate with multiple energized paths. They offer high continuity but require more complex power-flow analysis, fault interruption and directional protection. Dense urban secondary networks are important examples.

1.2 Feeders, distributors and substations

A feeder carries bulk power from a substation toward load areas and usually has limited intermediate tapping near its source. A distributor has many tapped loads, so current varies along its length. A service connection links the low-voltage distributor to an individual customer.

A distribution substation may include power transformers, buses, circuit breakers, protective relays, instrument transformers, capacitor banks, grounding equipment and supervisory control and data acquisition (SCADA). Its design must satisfy normal loading, contingency loading, short-circuit duty, maintainability, safety and future growth.

2. Electrical Models and Power-Flow Conventions

2.1 Three-phase complex power

For a balanced, positive-sequence three-phase system, let V_AN be the phase-A line-to-neutral voltage phasor and I_A the corresponding phase current phasor, with current defined positive into the receiving load. The total complex power is

Here, P is three-phase active power in watts, Q is three-phase reactive power in vars, j = √{-1}, and the asterisk denotes complex conjugation. Positive P and Q represent active- and reactive-power absorption under the load convention.

The magnitude relation is

where V_LL and I_L are RMS magnitudes. This magnitude equation does not specify the power-factor angle.

Care is required with phasors. In a balanced positive-sequence system, V_AB = √3V_AN∠30°. Therefore, writing S = √3V_ABI_A^* using the actual line-to-line phasor produces a 30° angular error. If line-to-line phasors are used, the reference displacement must be included explicitly:

Using S_3φ=3V_ANI_A^* is generally less ambiguous. These balanced formulas are inappropriate for significantly unbalanced systems, which should be represented phase by phase, including neutral and mutual impedances where relevant.

2.2 Approximate feeder voltage drop

Consider a balanced three-phase feeder with per-phase series impedance Z=R+jX. Shunt capacitance is neglected, and the receiving-end voltage angle difference is assumed small. Let P and Q be total three-phase power absorbed downstream. The approximate reduction in line-to-line voltage magnitude is

The units are consistent: Ω×W/V = V. The denominator may be taken as receiving or nominal voltage when the drop is small.

Under this convention, positive reactive-power absorption makes XQ positive and increases voltage drop. Reactive-power injection corresponds to negative net Q, reducing the drop and possibly causing voltage rise. Active-power export likewise corresponds to negative net P. Voltage rise occurs approximately when RP+XQ<0.

Worked Example 1: Feeder voltage drop and loss

A balanced 12.47 kV feeder has per-phase impedance 0.4+j0.3 Ω. It supplies a load of 1.2 MW and 0.4 Mvar. Neglect shunt capacitance.

Thus, the approximate receiving voltage is 12,470-48.12=12,421.88 V, and the percentage drop is 48.12/12,470×100=0.386%.

The current magnitude is

The three-phase conductor loss is

If an inverter injects 0.5 Mvar while the load remains unchanged, net reactive absorption becomes Q=0.4-0.5=-0.1 Mvar. The revised drop is

Reactive injection reduces the drop, but it does not produce a rise in this example because the positive active-power term remains dominant.

2.3 Exact radial branch-flow model

For a radial branch from bus i to bus j, define P_ij and Q_ij as sending-end branch powers, r_ij+jx_ij as branch impedance, v_i=|V_i|², and ℓ_ij=|I_ij|². Let p_j and q_j be net consumption at bus j; generation is represented by negative consumption. The single-phase equivalent branch-flow equations are

These DistFlow equations include series losses. They apply directly to a radial single-phase network or balanced per-phase equivalent. Three-phase unbalanced analysis requires phase-domain matrix models. Omitting the quadratic loss terms yields a linearized model useful for screening and optimization, but its accuracy declines under heavy loading or large voltage deviations.

A backward–forward sweep solves radial networks efficiently. The backward sweep accumulates currents or powers from terminal buses toward the source; the forward sweep updates voltages from the source outward. Meshed networks generally require Newton–Raphson, current-injection, compensation or other methods that enforce loop constraints.

3. Voltage Regulation and Loss Management

Customer and equipment voltages must remain within statutory or contractual limits. Voltage varies with feeder impedance, loading, power factor, DER output and regulator settings.

Common control devices include:

• On-load tap-changing transformers: change transformer ratio while energized.
• Step-voltage regulators: provide discrete feeder voltage adjustments.
• Shunt capacitor banks: inject reactive power and reduce upstream current.
• Smart inverters: provide volt–var, fixed power-factor or volt–watt control.
• Battery systems: alter both active and reactive power, subject to converter rating.

For an inverter with apparent-power rating S_r, active power P and reactive power Q, the capability constraint is

Thus, an inverter operating at full active-power rating may have no reactive-power headroom unless it is oversized or active output is curtailed.

Capacitor placement can reduce current and I²R loss, but excessive compensation may cause overvoltage, leading power factor or resonance. Coordinated control is essential because independent tap changers, capacitor controllers and inverters can interact or operate excessively.

Losses include conductor losses, transformer winding losses, transformer core losses and nontechnical losses. Energy-loss studies must use time-series loading because the loss of a conductor is proportional to current squared, not average current.

4. Reliability, Resilience and Automation

Reliability concerns the frequency and duration of supply interruptions under expected conditions. Resilience concerns preparation for, survival during and recovery from high-impact events such as wildfire, flood, cyberattack or widespread storm damage.

For N_T customers, let N_i be customers interrupted in event i and U_i its duration in hours. Standard sustained-interruption indices are

SAIFI has units of interruptions per customer-year, SAIDI has hours per customer-year, and CAIDI has hours per interruption. Definitions of sustained interruption and exclusions must follow the applicable regulator.

Expected energy not supplied can be estimated as

where L_i is interrupted load in kW and U_i is in hours, giving ENS in kWh.

Worked Example 2: Reliability indices

A utility serves 2,000 customers. During one year, sustained events produce 2,600 customer interruptions and 3,900 customer-interruption hours.

Automation can improve these indices through fault location, isolation and service restoration (FLISR). Reclosers and sectionalizers isolate the faulted section, while tie switches restore healthy sections if alternative feeders have adequate thermal and voltage capacity.

5. Distribution Protection

Protection must detect abnormal conditions, isolate the smallest practical section and preserve equipment and public safety. Typical devices include fuses, circuit breakers, reclosers, sectionalizers, overcurrent relays, earth-fault relays and differential relays.

In a radial feeder without substantial DER, fault current normally flows from the substation toward the fault. Time–current coordination arranges downstream devices to operate before upstream backup devices. Reclosers may clear temporary faults and coordinate with downstream fuses.

DER complicates this arrangement by introducing:

• bidirectional fault current;
• altered fault-current magnitude;
• sympathetic tripping of healthy feeders;
• loss of fuse–recloser coordination;
• unintentional islanding;
• fault levels that vary with operating mode.

Synchronous generators may supply several multiples of rated current initially. Inverter-based resources commonly limit current to a smaller multiple of rated current and control its phase according to their protection algorithms. Consequently, conventional overcurrent protection may become less sensitive in inverter-dominated islands.

Mitigations include directional overcurrent elements, differential protection, transfer trip, adaptive settings, voltage- and frequency-based functions, communications-assisted schemes and grounding studies. Protection settings must be verified for maximum and minimum fault-current conditions, grid-connected and islanded modes, and credible equipment outages.

6. Planning Distributed Energy Resources

A DER interconnection study evaluates whether a proposed resource can operate without unacceptable effects on voltage, thermal loading, protection, power quality or safety. Hosting capacity is the amount of DER that can be connected at specified locations without violating defined criteria or requiring major upgrades. It is not a single immutable feeder rating: it depends on location, load, resource output, control settings and study criteria.

Important constraints include:

1. steady-state overvoltage or undervoltage;
2. conductor and transformer thermal limits;
3. reverse flow through regulators or transformers;
4. rapid voltage changes and flicker;
5. harmonic distortion;
6. phase imbalance;
7. protection coordination and interrupting duty;
8. grounding and unintentional islanding.

Time-series analysis is often preferable to one extreme snapshot because PV output, demand and storage dispatch vary over time. Probabilistic studies can represent uncertain weather, adoption rates and customer behavior.

6.1 Electric-vehicle charging

Unmanaged charging can create evening peaks and overload local transformers. If N identical chargers have rated power P_c and coincidence factor f_c, a screening estimate is

This is a planning approximation, not a physical law; coincidence factors should be obtained from relevant usage data.

For 100 chargers rated at 7.2 kW with f_c=0.35, the coincident demand is 100×7.2×0.35=252 kW. Managed charging can delay or modulate charging according to feeder capacity, electricity price, departure time and required energy. Vehicle-to-grid operation may provide flexibility but introduces battery-warranty, communication, metering and user-consent issues.

6.2 Energy storage

For nonnegative charging and discharging powers P_c and P_d, a discrete energy-state model is

Here, E_t is stored energy in kWh, powers are in kW, ∆t is in hours, and η_c and η_d are charging and discharging efficiencies between zero and one. Practical optimization prevents simultaneous charging and discharging unless a model explicitly allows it for a justified reason.

Suppose a battery must deliver 500 kW for 2 h with η_d=0.92. The reduction in stored energy is 500×2/0.92=1,086.96 kWh. If operation is restricted to 10–90% state of charge, the nameplate energy must be at least 1,086.96/0.8=1,358.7 kWh, excluding degradation and reserve margins.

6.3 Demand response

Demand response changes consumption in response to prices, incentives or direct control. Dispatchable loads include HVAC, water heating, refrigeration, industrial processes and managed EV charging. Effective programs specify measurement baselines, customer override rights, rebound effects, communication failure behavior and compensation.

7. Microgrids and Islanded Operation

A microgrid is a group of interconnected loads and distributed resources within defined electrical boundaries that acts as a controllable entity relative to the wider grid. It may operate grid-connected or intentionally islanded.

Figure: A microgrid with a controllable point of common coupling, grid-forming source and prioritized loads.

7.1 Grid-following and grid-forming resources

A grid-following inverter synchronizes to an existing voltage waveform and normally controls current, active power and reactive power. It cannot by itself establish a stable dead-bus voltage.

A grid-forming inverter establishes a voltage and frequency reference and can support an island. Dispatchable synchronous machines may perform the same reference-forming function. An island must contain adequate grid-forming capability, energy reserve and fault-management capability.

7.2 Droop control

Parallel sources can share power using active-power/frequency and reactive-power/voltage droop:

Here, f₀ and V₀ are reference values, P₀ and Q₀ are reference powers, and positive coefficients m_p and n_q determine droop slopes. These equations describe a common inductive-network approximation; resistive low-voltage networks may require modified or virtual-impedance control.

Primary control stabilizes voltage and frequency rapidly. Secondary control restores deviations and corrects sharing errors. Tertiary control performs economic dispatch and coordinates interchange with the utility.

7.3 Islanding and resynchronization

An intentional islanding sequence commonly includes detecting the grid disturbance, opening the point-of-common-coupling breaker, establishing the grid-forming reference, balancing generation and load, shedding lower-priority loads if necessary, and maintaining reserves. Reconnection requires acceptable voltage magnitude, frequency, phase angle and phase sequence before the breaker closes.

Unintentional islanding is hazardous because a supposedly disconnected circuit may remain energized. Anti-islanding protection and communication-assisted transfer trip may therefore be required by interconnection rules.

8. Integrated Planning and Optimization

Distribution planning compares network reinforcement with non-wire alternatives such as storage, demand response, managed charging and DER control. A simplified planning objective is

subject to power-flow equations, voltage limits, thermal limits, equipment ratings, storage dynamics, reliability criteria and operating reserves. Because decisions occur over years while demand and technology costs are uncertain, planners use scenarios, sensitivity studies and staged investments.

A technically feasible least-cost plan is not automatically acceptable. It must also address land use, environmental effects, cybersecurity, interoperability, customer equity and regulatory obligations.

9. Illustrative Case: University Campus Microgrid

Background

This fictional case represents a university campus supplied by a 13.8 kV radial feeder. Peak campus demand is 4.2 MW and 1.2 Mvar. The per-phase feeder impedance is 0.25+j0.35 Ω. The campus plans 2 MW of PV, a 1 MW/2 MWh battery and managed EV charging. Critical loads total 1.4 MW.

Problem

The university seeks to reduce peak demand, maintain acceptable voltage, improve outage resilience and avoid compromising feeder protection.

Analysis

At peak demand, apparent power is

The approximate feeder voltage drop is

This is 106.52/13,800×100=0.772%. Current is approximately 4.368×10⁶/(√3×13,800)=182.75 A, producing feeder loss

During a high-PV period, assume PV supplies 2 MW, the battery discharges at 1 MW and inverter controls inject 0.6 Mvar. Net feeder demand becomes 1.2 MW and 0.6 Mvar. The revised drop is

The reduction follows from lower active demand and lower net reactive absorption. Separate minimum-load analysis is still necessary because strong PV export could cause voltage rise.

For islanding, conservative PV output is assumed to be 0.4 MW. A 1 MW dispatchable generator and a 1 MW battery can collectively supply the 1.4 MW critical load, but only if the battery has adequate state of charge. The 2 MWh rating does not guarantee indefinite operation; energy management must preserve reserve and shed noncritical loads.

Approach and Solution

The proposed scheme uses the battery inverter as the grid-forming source, retains the generator for extended outages, manages EV charging according to feeder capacity and applies PV volt–var control. A point-of-common-coupling relay supervises islanding and synchronism-check reconnection. Protection studies evaluate both strong-grid and low-fault-current island conditions. Critical buildings are placed on prioritized circuits with automatic load shedding.

Expected Outcome

The system reduces feeder peak demand and losses, provides short-duration ride-through and supports critical loads during longer outages when fuel is available. Its benefits depend on maintaining reserve, testing island transitions and coordinating inverter, regulator and relay settings.

Learning Points

1. Power capacity in MW and energy capacity in MWh solve different problems.
2. DER controls must be evaluated at peak load, minimum load and credible contingencies.
3. Resilience requires load prioritization, grid-forming capability and protection—not merely local generation.
4. Approximate calculations support screening, but final design requires unbalanced time-series and fault studies.

10. Governance, Ethics and Emerging Practice

Interconnection requirements commonly address voltage and frequency ride-through, reactive-power capability, anti-islanding, communications and testing. Standards such as IEEE 1547 provide influential frameworks, but engineers must use the edition and legal requirements adopted in the relevant jurisdiction.

Cybersecurity is essential because smart inverters, chargers, relays and energy-management systems are remotely accessible. Good practice includes network segmentation, authenticated communications, least-privilege access, secure firmware management, event logging and tested manual fallback procedures.

Ethical planning considers whether costs and benefits are distributed fairly. Poorly designed tariffs may shift network costs to customers unable to purchase DER. Demand-response systems must protect privacy and preserve reasonable customer control. Resilience investments should consider critical public services and vulnerable populations rather than only high-value private loads.

Contemporary developments include advanced distribution management systems, dynamic operating envelopes, grid-forming inverters, solid-state transformers and artificial intelligence for load forecasting, anomaly detection and predictive maintenance. AI outputs require validation, monitoring and human accountability because biased data or changing network conditions can produce unsafe recommendations.

Best-Practice Checklist

• Use explicit power-flow and reactive-power sign conventions.
• Model imbalance where single-phase loading or DER is significant.
• Evaluate peak load, minimum load, reverse flow and contingencies.
• Coordinate regulators, capacitors and inverter controls.
• Verify protection in grid-connected and islanded modes.
• Distinguish storage power rating from energy rating.
• Use time-series and probabilistic studies where variability matters.
• Test communications failure, black start and resynchronization procedures.
• Include cybersecurity, equity and regulatory compliance in technical decisions.

Chapter Summary

Distribution networks may be radial, looped or meshed, with different implications for cost, reliability and protection. Balanced feeder analysis uses consistent phase references and explicit load sign conventions. Positive reactive-power absorption increases voltage drop, whereas reactive injection reduces it and can cause rise when export is sufficiently large. DistFlow and backward–forward sweep methods provide stronger analysis of radial networks than simple voltage-drop approximations.

Voltage is controlled through transformer taps, regulators, capacitors and smart inverters. Reliability is quantified using SAIFI, SAIDI, CAIDI and energy-not-supplied measures, while resilience addresses severe disruptions and recovery. DER, EV charging and storage can reduce losses and peaks but may create reverse flow, thermal, voltage and protection problems. Microgrids require grid-forming capability, coordinated control, adequate energy reserves, intentional islanding logic and safe resynchronization. Effective planning integrates technical feasibility, economics, regulation, cybersecurity, environmental responsibility and equity.

Key Terms

Radial feeder: A feeder with one normal electrical path from source to customer.

Looped system: A network with an alternative path, often operated with a normally open tie.

Meshed network: A network with multiple energized paths between buses.

Distribution substation: A facility that transforms voltage and controls outgoing distribution circuits.

Voltage regulation: Control of voltage within required operating limits.

DistFlow: Branch-flow equations describing power, current, voltage and losses in radial networks.

Hosting capacity: DER capacity that can be accommodated under defined criteria without unacceptable violations.

Reverse power flow: Power flow from downstream generation toward the substation or upstream network.

Smart inverter: A power-electronic interface with configurable voltage, frequency and reactive-power functions.

SAIFI: Average number of sustained customer interruptions per year.

SAIDI: Average sustained interruption duration per customer per year.

CAIDI: Average duration per sustained customer interruption.

Grid-following inverter: An inverter that synchronizes to an externally established voltage waveform.

Grid-forming inverter: An inverter capable of establishing and regulating voltage and frequency.

Microgrid: A controllable group of loads and resources capable of grid-connected or islanded operation.

Droop control: Decentralized power-sharing control based on frequency–power and voltage–reactive-power relationships.

Demand response: Deliberate modification of demand in response to control signals, prices or incentives.

State of charge: Stored energy expressed as an absolute value or fraction of storage capacity.

FLISR: Automated fault location, isolation and service restoration.

Adaptive protection: Protection whose settings or logic change with network operating conditions.

Review Questions

Short Answer Questions

1. Distinguish a radial feeder from a closed-loop feeder.
2. Why must the phase reference be stated when calculating three-phase complex power?
3. How does reactive-power injection affect feeder voltage under the stated load convention?
4. Define SAIFI and SAIDI.
5. What is the difference between grid-following and grid-forming inverters?

Long Answer Questions

1. Explain how substations, feeders, distributors and service connections form a distribution system.
2. Derive the approximate balanced-feeder voltage-drop equation and state its assumptions.
3. Discuss how high DER penetration affects voltage regulation, losses and protection coordination.
4. Explain the control hierarchy and transition sequence of an islandable microgrid.
5. Compare network reinforcement with storage, demand response and managed charging as planning alternatives.

Analytical / Application Questions

1. A balanced 11 kV feeder with per-phase impedance 0.3+j0.25 Ω supplies 2 MW and 0.8 Mvar. Estimate line-to-line voltage drop, current and conductor loss.
2. Develop a coordinated charging strategy for 300 workplace EV chargers subject to a transformer limit, uncertain arrival times and customer departure requirements.
3. Design a conceptual protection and energy-management strategy for a hospital microgrid containing PV, battery storage and a standby generator.

Multiple Choice Questions with Answers

Question 1

Under the chapter's load sign convention, which condition increases approximate feeder voltage drop when all other quantities are unchanged?

A. Increasing positive reactive-power absorption

B. Increasing reactive-power injection

C. Reducing active-power absorption

D. Increasing downstream active-power export

Correct Answer: A. Increasing positive reactive-power absorption

Question 2

For a balanced positive-sequence system, which expression unambiguously gives total complex power using corresponding phase quantities?

A. S=V_ANI_A^*

B. S=3V_ANI_A^*

C. S=√3V_ABI_A^* without an angle correction

D. S=3V_ABI_A^*

Correct Answer: B. S=3V_ANI_A^*

Question 3

A balanced 10 kV feeder has per-phase R=0.2 Ω and X=0.3 Ω and supplies 1 MW and 0.5 Mvar. What is the approximate line-to-line voltage drop?

A. 15 V

B. 20 V

C. 35 V

D. 70 V

Correct Answer: C. 35 V

Question 4

Which distribution configuration normally provides only one energized path from the substation to each customer?

A. Closed mesh

B. Radial system

C. Secondary network

D. Closed ring

Correct Answer: B. Radial system

Question 5

A utility records 1,800 customer interruptions among 1,200 customers in one year. What is SAIFI?

A. 0.67 interruptions/customer-year

B. 1.20 interruptions/customer-year

C. 1.50 interruptions/customer-year

D. 2.16 interruptions/customer-year

Correct Answer: C. 1.50 interruptions/customer-year

Question 6

Which resource can establish a voltage and frequency reference for a dead island?

A. A grid-following inverter operating alone

B. An uncontrolled capacitor bank

C. A grid-forming inverter with an energized DC source

D. A passive harmonic filter

Correct Answer: C. A grid-forming inverter with an energized DC source

Question 7

A battery delivers 400 kW for 2 h at a discharge efficiency of 0.80. By how much does its stored energy decrease?

A. 640 kWh

B. 800 kWh

C. 1,000 kWh

D. 1,200 kWh

Correct Answer: C. 1,000 kWh

Question 8

Which statement best describes distribution hosting capacity?

A. It is always equal to the substation transformer nameplate rating.

B. It is independent of DER location and control settings.

C. It is the DER capacity accommodated under specified criteria without unacceptable violations or major upgrades.

D. It is the annual energy consumed by all downstream customers.

Correct Answer: C. It is the DER capacity accommodated under specified criteria without unacceptable violations or major upgrades.

Question 9

Why may conventional overcurrent protection become less sensitive in an inverter-dominated island?

A. Inverters commonly limit fault current.

B. Inverters always increase feeder reactance to infinity.

C. Islanded systems cannot experience electrical faults.

D. Overcurrent relays operate only on DC current.

Correct Answer: A. Inverters commonly limit fault current.

Question 10

One hundred 7.2 kW EV chargers have a coincidence factor of 0.35. What coincident demand is estimated by the screening formula?

A. 72 kW

B. 252 kW

C. 350 kW

D. 720 kW

Correct Answer: B. 252 kW