7.1 Volt-Ampere Characteristics, Operating Point, Self-Regulation & OCV Limits

7.1 Power Source Volt-Ampere Curves: CC vs CV & Self-Regulating Arcs

Quick Answer: Welding power sources are broadly divided into Constant Current (CC / drooper) and Constant Voltage (CV / flat) architectures based on the slope of their static output volt-ampere ($V-I$) characteristic curves ($dV/dI$). CC power sources exhibit a steep negative slope (typically $-10\text{ to }-25\text{ V}/100\text{ A}$), ensuring that manual arc length fluctuations produce minimal change in welding current, which is critical for Shielded Metal Arc Welding (SMAW) and Gas Tungsten Arc Welding (GTAW). Conversely, CV power sources have a flat output slope (typically $-1.5\text{ to }-3.0\text{ V}/100\text{ A}$), which produces instantaneous current spikes or drops in response to minor arc voltage changes. When paired with a constant-speed wire feeder in Gas Metal Arc Welding (GMAW) or Flux Cored Arc Welding (FCAW), this flat slope establishes an autonomous, negative-feedback self-regulating arc that dynamically matches wire melting rate to wire feed speed without external sensors.

---

1. Static Volt-Ampere (V-I) Characteristics: CC vs CV Architectures

The operating point of any electric arc welding circuit is established at the mathematical intersection of two independent electrical curves: the power source static volt-ampere output curve ($V_{\text{source}} = f(I)$) and the arc characteristic curve ($V_{\text{arc}} = f(I, L_{\text{arc}})$).

   Voltage (V)                                   Voltage (V)
        ^
    OCV +                                         OCV +
        | |                                           | |...... Constant Voltage (CV)
        | |                                           | |      Slope = -1.5 to -3.0 V/100A
        | |   Constant Current (CC)                   | |.... Operating Point
        | |   Slope = -10 to -25 V/100A               |      ......
     V0 +--|---------*----[ Arc Curve ]            V0 +-------------*------[ Arc Curve ]
        |   |       /                                 |            /
        |    |     /                                  |           /
        |     |   /                                   |          /
      0 +-------+----------------------> Current    0 +---------+---+------------------> Current
                I0                                             I0  I_sc

Constant Current (CC / "Drooper") Architecture

A Constant Current power source is engineered with a steep negative slope ($dV/dI$). In conventional transformer-rectifiers, this droop was achieved using high internal leakage reactance or moving iron cores; in modern inverters, digital closed-loop current feedback dynamically adjusts pulse-width modulation (PWM) to force the output along a near-vertical load line.

• Mathematical Model: Approximated linearly around the operating point as: $$V_{\text{source}} = V_{\text{oc}} - s_{\text{cc}} \cdot I$$ where $V_{\text{oc}}$ is the Open-Circuit Voltage ($60\text{ to }80\text{ V}$) and $s_{\text{cc}} = |dV/dI| \approx 0.10\text{ to }0.25\text{ V/A}$ ($10\text{ to }25\text{ V per }100\text{ A}$). Many modern inverter CC supplies provide near-vertical slopes ($s_{\text{cc}} > 1.0\text{ V/A}$).
• Arc Length Disturbance Response: If a manual welder's hand tremors cause the arc length to jump by $\Delta L = +1.5\text{ mm}$, the arc column voltage jumps by $\Delta V_{\text{arc}} \approx +3.0\text{ V}$ (assuming an electric field gradient $E_p \approx 2.0\text{ V/mm}$). Because the load line is steep: $$\Delta I = -\frac{\Delta V_{\text{arc}}}{s_{\text{cc}}} = -\frac{3.0\text{ V}}{0.20\text{ V/A}} = -15\text{ A}$$ In a nominal $150\text{ A}$ SMAW circuit, this represents only a $10\%$ change in current, preserving heat input, penetration depth, and preventing accidental arc extinction.

Constant Voltage (CV / "Flat") Architecture

A Constant Voltage power supply maintains a nearly flat load line with a gentle downward slope ($dV/dI$).

• Mathematical Model: $$V_{\text{source}} = V_{\text{oc}} - s_{\text{cv}} \cdot I$$ where $s_{\text{cv}} = |dV/dI| \approx 0.015\text{ to }0.030\text{ V/A}$ ($1.5\text{ to }3.0\text{ V per }100\text{ A}$). The slight droop is intentional: a zero-slope power source would experience catastrophic, infinite short-circuit current surges during droplet transfer.
• Arc Length Disturbance Response: If arc length increases by $1.5\text{ mm}$ ($\Delta V_{\text{arc}} \approx +3.0\text{ V}$), the resulting current drop is massive: $$\Delta I = -\frac{\Delta V_{\text{arc}}}{s_{\text{cv}}} = -\frac{3.0\text{ V}}{0.020\text{ V/A}} = -150\text{ A}$$ This massive current swing provides the physical mechanism for self-regulation in automated and semi-automatic wire feeding.

---

2. The Arc Characteristic Line & Operating Point Intersection

The welding arc does not possess a fixed electrical resistance; rather, its voltage is determined by the summation of the electrode fall regions and the column electric field:

$$V_{\text{arc}} = (V_c + V_a) + E_p \cdot L_{\text{arc}} + R_p(I) \cdot I$$

where $(V_c + V_a)$ is the sum of cathode and anode sheath voltage drops ($8\text{ to }16\text{ V}$), $E_p$ is the column electric field ($1.0\text{ to }2.5\text{ V/mm}$ depending on shielding gas), and $L_{\text{arc}}$ is physical arc length.

   Arc Voltage (V)
        ^
        |                     / [L_arc = 6 mm]  <-- Longer Arc (Higher Voltage)
        |                    / 
     V2 +-------------------*---/ [L_arc = 4 mm]  <-- Equilibrium Arc
        |                  /   / 
     V1 +-----------------*---*--/ [L_arc = 2 mm]  <-- Shorter Arc (Lower Voltage)
        |                /   /  / 
        |               /   *  / 
        |              /   /  / 
        |             /   /  /  
      0 +------------+---+---+-----------------> Welding Current (I)
                    I2  I0  I1

At typical industrial currents ($I > 100\text{ A}$), the arc volt-ampere characteristic displays a weakly positive incremental resistance ($dV_{\text{arc}}/dI > 0$) due to column thermal constriction and magnetic pinch effects. The steady-state operating point $(I_0, V_0)$ is the unique simultaneous solution where $V_{\text{source}}(I) = V_{\text{arc}}(I)$:

$$V_{\text{oc}} - s \cdot I_0 = V_0 = (V_c + V_a) + E_p \cdot L_{\text{arc}} + b \cdot I_0$$ $$I_0 = \frac{V_{\text{oc}} - (V_c + V_a) - E_p \cdot L_{\text{arc}}}{s + b}$$

---

3. The Self-Regulating Arc Feedback Loop in CV GMAW

In Gas Metal Arc Welding (GMAW) and Flux-Cored Arc Welding (FCAW), consumable electrode wire is driven into the weld puddle by a mechanical wire feeder operating at a preset, constant wire feed speed ($WFS = v_w$). The process remains stable only if the wire melting rate ($MR$) precisely equals the feed speed ($MR = WFS$).

The wire melting rate is governed by the Lesnewich equation, combining cathode/anode fall heating and Joule extension preheating:

$$MR = \alpha \cdot I + \beta \cdot L_{\text{ext}} \cdot I^2$$

where $\alpha$ is the arc heating melting coefficient, $\beta$ is the resistive preheating coefficient, and $L_{\text{ext}}$ is the electrode extension (stickout).

           +-----------------------------------------------------------+
           |  Equilibrium State: Wire Feed Speed (WFS) = Melt Rate (MR) |
           |               Arc Length = L0, Current = I0               |
           +-----------------------------------------------------------+
                                         |
                   [DISTURBANCE: Torch Contact-to-Work Distance Increases]
                                         |
                                         v
           +-----------------------------------------------------------+
           | Arc Length Increases (L_arc > L0)                         |
           | Arc Column Resistance Increases                           |
           +-----------------------------------------------------------+
                                         |
                                         v
           +-----------------------------------------------------------+
           | Arc Voltage Rises: V_arc = V0 + Delta V                   |
           +-----------------------------------------------------------+
                                         |
                                         v
           +-----------------------------------------------------------+
           | CV Load Line Forces Sharp Current Drop:                   |
           | Delta I = -Delta V / s_cv  (Instantaneous Drop: 50-150 A) |
           +-----------------------------------------------------------+
                                         |
                                         v
           +-----------------------------------------------------------+
           | Wire Melt Rate Plummets:                                  |
           | MR = alpha*I + beta*L_ext*I^2  ==>  MR < WFS              |
           +-----------------------------------------------------------+
                                         |
                                         v
           +-----------------------------------------------------------+
           | Constant WFS Drives Wire Forward Faster Than It Melts:    |
           | dL_arc / dt = MR - WFS < 0                                |
           | Arc Length Collapses Back to Equilibrium (L_arc -> L0)    |
           +-----------------------------------------------------------+
                                         |
                                         v
           +-----------------------------------------------------------+
           | RESTORATION: Operating Point Returns to (I0, V0)          |
           +-----------------------------------------------------------+ 

Why Process Pairing Cannot Be Inverted

• CV with Manual SMAW / GTAW: If a welder uses a CV power source for manual GTAW or SMAW, the slightest unsteadiness in hand position ($1\text{ mm}$ movement) would generate a massive $50\text{ to }100\text{ A}$ current surge or drop. The arc would either instantly burn through the sheet metal or violently freeze the electrode into the weld pool.
• CC with Fixed-Speed GMAW: If a constant-speed wire feeder is connected to a CC power source, the power source will maintain fixed current regardless of arc length. If the arc length lengthens, current will not drop, melting rate will not decrease, and the wire will continue melting back until it burns back into the copper contact tip, destroying it.
• Voltage-Sensing Wire Feeders (VSW) on CC: When field GMAW or FCAW must be performed using engine-driven CC power sources, a voltage-sensing wire feeder is required. The feeder monitors arc voltage across the torch and ground leads; if arc length lengthens (voltage rises), the feeder's internal DC drive motor dynamically speeds up to push the wire forward, mechanically replicating self-regulation.

---

4. Open-Circuit Voltage (OCV) Safety Standards & Short-Circuit Behavior

ANSI Z49.1 & NEMA EW-1 Regulatory Standards

Open-circuit voltage ($V_{\text{oc}}$) is the potential measured across the output terminals when the power source is energized but no arc is established ($I = 0$). High OCV promotes reliable arc striking and ionization of the gas path, but poses severe electrocution risks to the welding operator.

CWEng Exam Distinction: Voltage Reducing Devices (VRDs) are mandated in many jurisdictions for SMAW. A VRD senses when no arc is struck and clamps the terminal OCV to a safe level ($<15\text{ to }24\text{ V}$). Within milliseconds of the electrode touching the workpiece, the VRD switches off, allowing full OCV to establish the arc.

Short-Circuit Current ($I_{\text{sc}}$) Behavior

When an electrode stubs directly into the base metal, arc length becomes zero ($L_{\text{arc}} = 0$) and resistance drops to the metallic loop resistance:

• On a CV supply, theoretical short-circuit current is governed by the slope: $I_{\text{sc}} = V_{\text{oc}} / s_{\text{cv}}$. For $V_{\text{oc}} = 36\text{ V}$ and $s_{\text{cv}} = 0.02\text{ V/A}$, $I_{\text{sc}} = 1800\text{ A}$. Internal electronic current limiters or inductors must clamp this spike to prevent exploding the wire.
• On a CC supply, short-circuit current is constrained by the steep droop. Modern CC units feature an Arc Force (Dig) control that dynamically boosts current by $20\text{ to }50\%$ only when voltage drops below $14\text{ to }18\text{ V}$, preventing electrode freezing during tight SMAW root-pass manipulation without causing gross overheating.

---