ZIPload

Thus far the loads on the systems we’ve been modeling have been fairly abstract and relatively simple, with only a constant power load on a single phase being specified. A more general form of this type of load is often referred to as a ZIP load which is represented as a load with three distinct parts:

• a constant impedance portion \(Z\),
• a constant current portion \(I\), and
• a constant power portion \(P\).

Each of these portions respond differently to changes in load voltage based on their first-principles models: \(P=I^2Z\), \(P = IV\), and \(P = P\). For a reduction in system voltage, we would expect the following:

• For constant impedance (\(Z\)), the power would be reduced as the square of the voltage change, and the current (\(I\)) would be reduced linearly according to the voltage change.

• For constant current (\(I\)), both the power and the current would be reduced linearly with the voltage change.

• For constant power (\(P\)), the power will remain unchanged and the current will increase linearly with the voltage change.

In parallel with the real power components, ZIP loading can also be applied to the reactive power component; that is, these loads can all be expressed as complex values in GridLAB-D™, as you have seen in previous examples. In a three phase system, the load on each phase can be described independently, giving a total of nine complex load values to fully define a three-phase load.

GridLAB-D™ also has an alternative and perhaps slightly more complex means of representing the same load using the same principles. Rather than specifying the portions of the load directly as three individual complex loads (per phase), a nominal “base” complex load value can be given and is then modified with three power-factor values (constant impedance, current and power power-factors) and an additional three load-fraction values (what portion of the load is constant impedance, current, and power). Mathematically, these two means of defining ZIP loads are identical.

Example - ZIP loads

Open the model zip_loads.glm you'll see a slight variation on a version of the model we've used in the tutorial. The main modification made to the file is the creation of an additional load at branch_1_meter_1 in parallel to the original. These two loads have both been moved downstream of the main branch by the creation of load_node which connects to each of the two loads' meters through very short overhead lines.

    ...

    object load {
            parent branch_1_meter_1a;
            name b1m1_load_a;
            nominal_voltage 7216.88;
            phases ABC;
                    constant_power_A 30000+40000j;
                    constant_current_A 10+10j;
                    constant_impedance_A 1000+500j;
    }

    ...

    object load {
            parent branch_1_meter_1b;
            name b1m1_load_b;
            nominal_voltage 7216.88;
            phases ABC;
                    base_power_A 190 kVA;
                    power_fraction_A 0.26;  
                    current_fraction_A 0.51;  
                    impedance_fraction_A 0.23;   
                    power_pf_A 0.60;
                    current_pf_A -0.71;
                    impedance_pf_A 0.91;
    }

Looking at the two loads, you'll see that b1m1_load_a is defined in terms of the constant_power, constant_current, and constant_voltage. The default units for these value are W, A, and Ohms, respectively. Load b1m1_load_b has a very similar composite load but it is defined in the alternative style mentioned above. Running a simulation using this model and opening "meter_powers.csv" reveals that both of these loads have similar power over the duration of the simulation, at least to the precision of the values entered.

Modeling Approach

The ZIPload model is designed to provide a means to access the residential enduse class at a fundamental level and from a "power engineer" perspective. It uses a classic ZIP load model (constant impedance, current, and power) where "base power" is specified, then the ZIP fractions and power factors are assigned. The ZIP model equations can be defined as:

where:

• \(P_i\): Real power consumption of the ith load
• \(Q_i\): Reactive power consumption of the ith load
• \(V_a\): Actual terminal voltage
• \(V_n\): Nominal terminal voltage
• \(S_n\): Apparent Power consumption at nominal voltage
• \(Z_\%\): Percent of load that is constant impedance
• \(I_\%\): Percent of load that is constant current
• \(P_\%\): Percent of load that is constant power
• \(Z_\theta\): Phase angle of constant impedance fraction
• \(I_\theta\): Phase angle of constant current fraction
• \(P_\theta\): Phase angle of constant power fraction

In a time-variant load representation, the coefficients of the ZIP model, \(V_n, S_n, Z_\%, I_\%, P_\%, Z_\theta, I_\theta\), and \(P_\theta\) remain constant, but the power consumption, \(P_i\) and \(Q_i\), of the ith load varies with the actual terminal voltage, \(V_a\). The ZIP model is similar to the polynomial representation used in many commercial software packages. In the polynomial representation of the ZIP load, the constant coefficient is roughly equivalent to the P fraction, the linear coefficient is roughly equivalent to the I fraction, and the quadratic coefficient is roughly equivalent to the Z fraction. The ZIP model only varies the power consumption as a function of actual terminal voltage, \(V_a\). Note also that the sum of \(Z_\%, I_\%,\) and \(P_\%\) must equal one.

Internally, the model performs all of the proper phase rotations and scaling for various voltage levels (e.g., the model would look the same for a house attached on Phase A versus Phase C). The ZIPload model applies ZIP voltage scaling using the attached circuit voltage magnitude and the default line voltage. Currently, it is assumed that nominal voltage is either 120 or 240 V.

Parameters

Mode behavior

The ZIPload object supports several operating modes that can be combined.

Base ZIP behavior

• The object computes three complex power terms each sync: constant-power, constant-current, and constant-impedance.

• base_power is split by power_fraction, current_fraction, and impedance_fraction.

• power_pf, current_pf, and impedance_pf set each term's reactive component.
• actual_power is voltage-adjusted as:

where \(V_f\) is the per-unit terminal voltage (load.voltage_factor).

Cycling mode

Enabled by duty_cycle/period/phase

• Cycling is enabled when duty_cycle != -1.
• Validation rules in init:
• duty_cycle must be in [0,1],
• period > 0,
• phase must be in [0,1].
• Internally, the model advances phase each sync and toggles multiplier between 0 and 1 as the on/off window changes.
• next_time is scheduled to the next transition boundary, so event timing aligns with cycle edges.

Demand response equilibrium mode [Experimental]

Enabled by demand_response_mode=true

• The object represents a population of devices using N devices across L temperature bins.
• Per-sync updates compute transitions between drm.on and drm.off using:
  • ron (rate of heating),
  • roff (rate of cooling),
  • eta (demand rate disturbance).
• Aggregate state outputs are updated:
  • number_of_devices_on (N_on),
  • number_of_devices_off (N_off),
  • phi = roff/(ron+roff),
  • nominal_power = base_power * N_on / N.
• In this mode, electrical demand uses nominal_power rather than multiplier * base_power.

Aggregate interpretation

• In practice, aggregate mode is the same population formulation used by demand_response_mode.
• Can model many similar devices as one ZIPload object by setting number_of_devices and DR parameters, then observe aggregate variables (N_on, N_off, nominal_power, phi).
• Setting eta = 0 yields the no-disturbance equilibrium update path (uniform behavior); nonzero eta applies a demand disturbance.

Override and recovery interaction

• ZIPload inherits override (NORMAL, ON, OFF) from residential_enduse.
• In duty-cycle operation, override changes how the cycle is applied:
  • NORMAL: follow duty_cycle,
  • OFF: use recovery_duty_cycle transition logic,
  • ON: hold load suppressed behavior according to override branch logic.
• This is why controller examples often bind state_property to multiplier or override.

Example models

Simple ZIPload with Schedule

This model is representative of a simple ZIPload with scheduled load behavior.

object ZIPload {
        name house1_load;
        parent house1;
        base_power responsive_loads*1.06;
        heatgain_fraction 0.90;
        power_pf 1.0;
        current_pf 1.0;
        impedance_pf 1.0;
        impedance_fraction 0.20;
        current_fraction 0.40;
        power_fraction 0.40;
};

ZIPload using Cycling Mode

This model is representative of a ZIPload used in cycling mode to roughly represent a schedule pool pump (note, pool_pump_season is a schedule comprised of 0 or 1 values).

object ZIPload {
        name house1_poolpump;
        parent house1;
        base_power pool_pump_season*1.44;
        duty_cycle 0.22;
        phase 0.26;
        period 4.96;
        heatgain_fraction 0.0;
        power_pf 1.0;
        current_pf 1.0;
        impedance_pf 1.0;
        impedance_fraction 0.20;
        current_fraction 0.40;
        power_fraction 0.40;
        is_240 TRUE;
};

ZIPload with Passive Controller

This model is representative of a ZIPload with a passive controller used to implement the elasticity model out of the market module.

object ZIPload {
        name house1_load;
        parent house1;
        base_power responsive_loads*1.06;
        heatgain_fraction 0.90;
        power_pf 1.0;
        current_pf 1.0;
        impedance_pf 1.0;
        impedance_fraction 0.20;
        current_fraction 0.40;
        power_fraction 0.40;
        object passive_controller {
            period 900;
            control_mode ELASTICITY_MODEL;
            two_tier_cpp true;
            observation_object Market_1;
            observation_property past_market.clearing_price;
            state_property multiplier;
            linearize_elasticity true;
            price_offset 0.01;
            critical_day CPP_days_R1.value;
            first_tier_hours 12;
            second_tier_hours 12;
            third_tier_hours 6;
            first_tier_price 0.060483;
            second_tier_price 0.120965;
            third_tier_price 0.604826;
            old_first_tier_price 0.124300;
            old_second_tier_price 0.124300;
            old_third_tier_price 0.124300;
            daily_elasticity daily_elasticity_wtech*1.1731;
            sub_elasticity_first_second -0.1783;
            sub_elasticity_first_third -0.2604;
        };
};

Demand Response Enabled ZIPload with Pool Pump

This model is representative of a "pool pump" or cycling model that is using a DR control from the market module.

object ZIPload {
        name house1_poolpump;
        parent house1;
        base_power pool_pump_season*1.44;
        duty_cycle 0.22;
        phase 0.26;
        period 4.96;
        heatgain_fraction 0.0;
        power_pf 1.0;
        current_pf 1.0;
        impedance_pf 1.0;
        impedance_fraction 0.20;
        current_fraction 0.40;
        power_fraction 0.40;
        is_240 TRUE;
        recovery_duty_cycle 0.27;
        object passive_controller {
            period 900;
            control_mode DUTYCYCLE;
            pool_pump_model true;
            observation_object Market_1;
            observation_property past_market.clearing_price;
            state_property override;
            base_duty_cycle 0.22;
            setpoint duty_cycle;
            first_tier_hours 12;
            second_tier_hours 12;
            third_tier_hours 6;
            first_tier_price 0.060483;
            second_tier_price 0.120965;
            third_tier_price 0.604826;
        };
};

Cycling-only ZIPload (no market controller)

This mode uses an internal on/off cycle with no external controller. The load toggles by updating multiplier from the cycle state.

object ZIPload {
            name zip_cycling_only;
            parent house1;
            base_power 1.8;
            duty_cycle 0.35;
            period 2.0;
            phase 0.15;
            power_pf 0.98;
            current_pf 0.98;
            impedance_pf 0.98;
            impedance_fraction 0.20;
            current_fraction 0.30;
            power_fraction 0.50;
};

ZIPloads in Aggregate population mode (equilibrium, no disturbance)

This represents many similar devices as one aggregate ZIPload using the DR state equations with eta = 0.

object ZIPload {
            name zip_aggregate;
            parent house1;
            base_power 75.0;
            demand_response_mode TRUE;
            number_of_devices 300;
            thermostatic_control_range 20;
            rate_of_cooling 1.2;
            rate_of_heating 1.8;
            phi 0.45;
            demand_rate 0.0;
            power_pf 0.95;
            current_pf 0.95;
            impedance_pf 0.95;
            impedance_fraction 0.20;
            current_fraction 0.30;
            power_fraction 0.50;
};

ZIPload in Aggregate demand-response mode (disturbance enabled)

This applies a nonzero demand disturbance and lets the model evolve number_of_devices_on/off and nominal_power over time.

object ZIPload {
            name zip_aggregate_dr;
            parent house1;
            base_power 75.0;
            demand_response_mode TRUE;
            number_of_devices 300;
            thermostatic_control_range 20;
            rate_of_cooling 1.2;
            rate_of_heating 1.8;
            phi 0.45;
            demand_rate 0.15;
            power_pf 0.95;
            current_pf 0.95;
            impedance_pf 0.95;
            impedance_fraction 0.20;
            current_fraction 0.30;
            power_fraction 0.50;
};

For DR runs, monitor number_of_devices_on, number_of_devices_off, phi, and nominal_power to verify aggregate state evolution.

ZIPload State of Development

ZIPload is considered a simple, stable model, with many layers of functionality.

Related Concepts:

• Powerflow User Guide
• Residential module
  • house class – Single-family home model.
  • residential_enduse class – Abstract residential end use class.
  • occupantload – Residential occupants (sensible and latent heat).
  • ZIPload – Generic constant impedance/current/power end use load.